National Association of Wine Retailers Release Letter Delivered to Attorneys General and Alcohol Regulatory Chiefs Concerning Unconstitutional and Unenforceable Wine Shipping Bans

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Web and mobile applications enhance efficiency and data accuracy using satellite maps and offline capabilities.

(PRWeb April 23, 2020)

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Ammunition Depot comments on Judge Roger T. Benitez ruling that Californians may again purchase ammo without a background check and order ammo online.

(PRWeb April 24, 2020)

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Niansheng Tang, Xiaodong Yan, Xingqiu Zhao.

Source: The Annals of Statistics, Volume 48, Number 1, 607--627.

Abstract:
This article considers simultaneous variable selection and parameter estimation as well as hypothesis testing in censored survival models where a parametric likelihood is not available. For the problem, we utilize certain growing dimensional general estimating equations and propose a penalized generalized empirical likelihood, where the general estimating equations are constructed based on the semiparametric efficiency bound of estimation with given moment conditions. The proposed penalized generalized empirical likelihood estimators enjoy the oracle properties, and the estimator of any fixed dimensional vector of nonzero parameters achieves the semiparametric efficiency bound asymptotically. Furthermore, we show that the penalized generalized empirical likelihood ratio test statistic has an asymptotic central chi-square distribution. The conditions of local and restricted global optimality of weighted penalized generalized empirical likelihood estimators are also discussed. We present a two-layer iterative algorithm for efficient implementation, and investigate its convergence property. The performance of the proposed methods is demonstrated by extensive simulation studies, and a real data example is provided for illustration.

Jere Koskela, Paul A. Jenkins, Adam M. Johansen, Dario Spanò.

Source: The Annals of Statistics, Volume 48, Number 1, 560--583.

Abstract:
We study weighted particle systems in which new generations are resampled from current particles with probabilities proportional to their weights. This covers a broad class of sequential Monte Carlo (SMC) methods, widely-used in applied statistics and cognate disciplines. We consider the genealogical tree embedded into such particle systems, and identify conditions, as well as an appropriate time-scaling, under which they converge to the Kingman $n$-coalescent in the infinite system size limit in the sense of finite-dimensional distributions. Thus, the tractable $n$-coalescent can be used to predict the shape and size of SMC genealogies, as we illustrate by characterising the limiting mean and variance of the tree height. SMC genealogies are known to be connected to algorithm performance, so that our results are likely to have applications in the design of new methods as well. Our conditions for convergence are strong, but we show by simulation that they do not appear to be necessary.

Eric D. Kolaczyk, Lizhen Lin, Steven Rosenberg, Jackson Walters, Jie Xu.

Source: The Annals of Statistics, Volume 48, Number 1, 514--538.

Abstract:
It is becoming increasingly common to see large collections of network data objects, that is, data sets in which a network is viewed as a fundamental unit of observation. As a result, there is a pressing need to develop network-based analogues of even many of the most basic tools already standard for scalar and vector data. In this paper, our focus is on averages of unlabeled, undirected networks with edge weights. Specifically, we (i) characterize a certain notion of the space of all such networks, (ii) describe key topological and geometric properties of this space relevant to doing probability and statistics thereupon, and (iii) use these properties to establish the asymptotic behavior of a generalized notion of an empirical mean under sampling from a distribution supported on this space. Our results rely on a combination of tools from geometry, probability theory and statistical shape analysis. In particular, the lack of vertex labeling necessitates working with a quotient space modding out permutations of labels. This results in a nontrivial geometry for the space of unlabeled networks, which in turn is found to have important implications on the types of probabilistic and statistical results that may be obtained and the techniques needed to obtain them.

Vladimir Koltchinskii, Matthias Löffler, Richard Nickl.

Source: The Annals of Statistics, Volume 48, Number 1, 464--490.

Abstract:
We study principal component analysis (PCA) for mean zero i.i.d. Gaussian observations $X_{1},dots,X_{n}$ in a separable Hilbert space $mathbb{H}$ with unknown covariance operator $Sigma $. The complexity of the problem is characterized by its effective rank $mathbf{r}(Sigma):=frac{operatorname{tr}(Sigma)}{|Sigma |}$, where $mathrm{tr}(Sigma)$ denotes the trace of $Sigma $ and $|Sigma|$ denotes its operator norm. We develop a method of bias reduction in the problem of estimation of linear functionals of eigenvectors of $Sigma $. Under the assumption that $mathbf{r}(Sigma)=o(n)$, we establish the asymptotic normality and asymptotic properties of the risk of the resulting estimators and prove matching minimax lower bounds, showing their semiparametric optimality.

Changliang Zou, Guanghui Wang, Runze Li.

Source: The Annals of Statistics, Volume 48, Number 1, 413--439.

Abstract:
In multiple change-point analysis, one of the major challenges is to estimate the number of change-points. Most existing approaches attempt to minimize a Schwarz information criterion which balances a term quantifying model fit with a penalization term accounting for model complexity that increases with the number of change-points and limits overfitting. However, different penalization terms are required to adapt to different contexts of multiple change-point problems and the optimal penalization magnitude usually varies from the model and error distribution. We propose a data-driven selection criterion that is applicable to most kinds of popular change-point detection methods, including binary segmentation and optimal partitioning algorithms. The key idea is to select the number of change-points that minimizes the squared prediction error, which measures the fit of a specified model for a new sample. We develop a cross-validation estimation scheme based on an order-preserved sample-splitting strategy, and establish its asymptotic selection consistency under some mild conditions. Effectiveness of the proposed selection criterion is demonstrated on a variety of numerical experiments and real-data examples.

Davy Paindaveine, Julien Remy, Thomas Verdebout.

Source: The Annals of Statistics, Volume 48, Number 1, 324--345.

Abstract:
We consider the problem of testing, on the basis of a $p$-variate Gaussian random sample, the null hypothesis $mathcal{H}_{0}:oldsymbol{ heta}_{1}=oldsymbol{ heta}_{1}^{0}$ against the alternative $mathcal{H}_{1}:oldsymbol{ heta}_{1} eq oldsymbol{ heta}_{1}^{0}$, where $oldsymbol{ heta}_{1}$ is the “first” eigenvector of the underlying covariance matrix and $oldsymbol{ heta}_{1}^{0}$ is a fixed unit $p$-vector. In the classical setup where eigenvalues $lambda_{1}>lambda_{2}geq cdots geq lambda_{p}$ are fixed, the Anderson ( Ann. Math. Stat. 34 (1963) 122–148) likelihood ratio test (LRT) and the Hallin, Paindaveine and Verdebout ( Ann. Statist. 38 (2010) 3245–3299) Le Cam optimal test for this problem are asymptotically equivalent under the null hypothesis, hence also under sequences of contiguous alternatives. We show that this equivalence does not survive asymptotic scenarios where $lambda_{n1}/lambda_{n2}=1+O(r_{n})$ with $r_{n}=O(1/sqrt{n})$. For such scenarios, the Le Cam optimal test still asymptotically meets the nominal level constraint, whereas the LRT severely overrejects the null hypothesis. Consequently, the former test should be favored over the latter one whenever the two largest sample eigenvalues are close to each other. By relying on the Le Cam’s asymptotic theory of statistical experiments, we study the non-null and optimality properties of the Le Cam optimal test in the aforementioned asymptotic scenarios and show that the null robustness of this test is not obtained at the expense of power. Our asymptotic investigation is extensive in the sense that it allows $r_{n}$ to converge to zero at an arbitrary rate. While we restrict to single-spiked spectra of the form $lambda_{n1}>lambda_{n2}=cdots =lambda_{np}$ to make our results as striking as possible, we extend our results to the more general elliptical case. Finally, we present an illustrative real data example.

Xiaoqin Wang, Li Yin.

Source: The Annals of Statistics, Volume 48, Number 1, 138--160.

Abstract:
In sequential causal inference, two types of causal effects are of practical interest, namely, the causal effect of the treatment regime (called the sequential causal effect) and the blip effect of treatment on the potential outcome after the last treatment. The well-known $G$-formula expresses these causal effects in terms of the standard parameters. In this article, we obtain a new $G$-formula that expresses these causal effects in terms of the point observable effects of treatments similar to treatment in the framework of single-point causal inference. Based on the new $G$-formula, we estimate these causal effects by maximum likelihood via point observable effects with methods extended from single-point causal inference. We are able to increase precision of the estimation without introducing biases by an unsaturated model imposing constraints on the point observable effects. We are also able to reduce the number of point observable effects in the estimation by treatment assignment conditions.

Xinran Li, Peng Ding, Donald B. Rubin.

Source: The Annals of Statistics, Volume 48, Number 1, 43--63.

Abstract:
With many pretreatment covariates and treatment factors, the classical factorial experiment often fails to balance covariates across multiple factorial effects simultaneously. Therefore, it is intuitive to restrict the randomization of the treatment factors to satisfy certain covariate balance criteria, possibly conforming to the tiers of factorial effects and covariates based on their relative importances. This is rerandomization in factorial experiments. We study the asymptotic properties of this experimental design under the randomization inference framework without imposing any distributional or modeling assumptions of the covariates and outcomes. We derive the joint asymptotic sampling distribution of the usual estimators of the factorial effects, and show that it is symmetric, unimodal and more “concentrated” at the true factorial effects under rerandomization than under the classical factorial experiment. We quantify this advantage of rerandomization using the notions of “central convex unimodality” and “peakedness” of the joint asymptotic sampling distribution. We also construct conservative large-sample confidence sets for the factorial effects.

Francesco Bravo, Juan Carlos Escanciano, Ingrid Van Keilegom.

Source: The Annals of Statistics, Volume 48, Number 1, 1--26.

Abstract:
In both parametric and certain nonparametric statistical models, the empirical likelihood ratio satisfies a nonparametric version of Wilks’ theorem. For many semiparametric models, however, the commonly used two-step (plug-in) empirical likelihood ratio is not asymptotically distribution-free, that is, its asymptotic distribution contains unknown quantities, and hence Wilks’ theorem breaks down. This article suggests a general approach to restore Wilks’ phenomenon in two-step semiparametric empirical likelihood inferences. The main insight consists in using as the moment function in the estimating equation the influence function of the plug-in sample moment. The proposed method is general; it leads to a chi-squared limiting distribution with known degrees of freedom; it is efficient; it does not require undersmoothing; and it is less sensitive to the first-step than alternative methods, which is particularly appealing for high-dimensional settings. Several examples and simulation studies illustrate the general applicability of the procedure and its excellent finite sample performance relative to competing methods.

Monika Bhattacharjee, Arup Bose.

Source: The Annals of Statistics, Volume 47, Number 6, 3470--3503.

Abstract:
Consider a high-dimensional linear time series model where the dimension $p$ and the sample size $n$ grow in such a way that $p/n o 0$. Let $hat{Gamma }_{u}$ be the $u$th order sample autocovariance matrix. We first show that the LSD of any symmetric polynomial in ${hat{Gamma }_{u},hat{Gamma }_{u}^{*},ugeq 0}$ exists under independence and moment assumptions on the driving sequence together with weak assumptions on the coefficient matrices. This LSD result, with some additional effort, implies the asymptotic normality of the trace of any polynomial in ${hat{Gamma }_{u},hat{Gamma }_{u}^{*},ugeq 0}$. We also study similar results for several independent MA processes. We show applications of the above results to statistical inference problems such as in estimation of the unknown order of a high-dimensional MA process and in graphical and significance tests for hypotheses on coefficient matrices of one or several such independent processes.

Alessandro Rinaldo, Larry Wasserman, Max G’Sell.

Source: The Annals of Statistics, Volume 47, Number 6, 3438--3469.

Abstract:
Several new methods have been recently proposed for performing valid inference after model selection. An older method is sample splitting: use part of the data for model selection and the rest for inference. In this paper, we revisit sample splitting combined with the bootstrap (or the Normal approximation). We show that this leads to a simple, assumption-lean approach to inference and we establish results on the accuracy of the method. In fact, we find new bounds on the accuracy of the bootstrap and the Normal approximation for general nonlinear parameters with increasing dimension which we then use to assess the accuracy of regression inference. We define new parameters that measure variable importance and that can be inferred with greater accuracy than the usual regression coefficients. Finally, we elucidate an inference-prediction trade-off: splitting increases the accuracy and robustness of inference but can decrease the accuracy of the predictions.

Victor Veitch, Daniel M. Roy.

Source: The Annals of Statistics, Volume 47, Number 6, 3274--3299.

Abstract:
Sparse exchangeable graphs on $mathbb{R}_{+}$, and the associated graphex framework for sparse graphs, generalize exchangeable graphs on $mathbb{N}$, and the associated graphon framework for dense graphs. We develop the graphex framework as a tool for statistical network analysis by identifying the sampling scheme that is naturally associated with the models of the framework, formalizing two natural notions of consistent estimation of the parameter (the graphex) underlying these models, and identifying general consistent estimators in each case. The sampling scheme is a modification of independent vertex sampling that throws away vertices that are isolated in the sampled subgraph. The estimators are variants of the empirical graphon estimator, which is known to be a consistent estimator for the distribution of dense exchangeable graphs; both can be understood as graph analogues to the empirical distribution in the i.i.d. sequence setting. Our results may be viewed as a generalization of consistent estimation via the empirical graphon from the dense graph regime to also include sparse graphs.

Xiaohui Chen, Kengo Kato.

Source: The Annals of Statistics, Volume 47, Number 6, 3127--3156.

Abstract:
This paper studies inference for the mean vector of a high-dimensional $U$-statistic. In the era of big data, the dimension $d$ of the $U$-statistic and the sample size $n$ of the observations tend to be both large, and the computation of the $U$-statistic is prohibitively demanding. Data-dependent inferential procedures such as the empirical bootstrap for $U$-statistics is even more computationally expensive. To overcome such a computational bottleneck, incomplete $U$-statistics obtained by sampling fewer terms of the $U$-statistic are attractive alternatives. In this paper, we introduce randomized incomplete $U$-statistics with sparse weights whose computational cost can be made independent of the order of the $U$-statistic. We derive nonasymptotic Gaussian approximation error bounds for the randomized incomplete $U$-statistics in high dimensions, namely in cases where the dimension $d$ is possibly much larger than the sample size $n$, for both nondegenerate and degenerate kernels. In addition, we propose generic bootstrap methods for the incomplete $U$-statistics that are computationally much less demanding than existing bootstrap methods, and establish finite sample validity of the proposed bootstrap methods. Our methods are illustrated on the application to nonparametric testing for the pairwise independence of a high-dimensional random vector under weaker assumptions than those appearing in the literature.

Reinhard Heckel, Nihar B. Shah, Kannan Ramchandran, Martin J. Wainwright.

Source: The Annals of Statistics, Volume 47, Number 6, 3099--3126.

Abstract:
We consider sequential or active ranking of a set of $n$ items based on noisy pairwise comparisons. Items are ranked according to the probability that a given item beats a randomly chosen item, and ranking refers to partitioning the items into sets of prespecified sizes according to their scores. This notion of ranking includes as special cases the identification of the top-$k$ items and the total ordering of the items. We first analyze a sequential ranking algorithm that counts the number of comparisons won, and uses these counts to decide whether to stop, or to compare another pair of items, chosen based on confidence intervals specified by the data collected up to that point. We prove that this algorithm succeeds in recovering the ranking using a number of comparisons that is optimal up to logarithmic factors. This guarantee does depend on whether or not the underlying pairwise probability matrix, satisfies a particular structural property, unlike a significant body of past work on pairwise ranking based on parametric models such as the Thurstone or Bradley–Terry–Luce models. It has been a long-standing open question as to whether or not imposing these parametric assumptions allows for improved ranking algorithms. For stochastic comparison models, in which the pairwise probabilities are bounded away from zero, our second contribution is to resolve this issue by proving a lower bound for parametric models. This shows, perhaps surprisingly, that these popular parametric modeling choices offer at most logarithmic gains for stochastic comparisons.

Zhou Fan, Iain M. Johnstone.

Source: The Annals of Statistics, Volume 47, Number 5, 2855--2886.

Abstract:
We study the spectra of MANOVA estimators for variance component covariance matrices in multivariate random effects models. When the dimensionality of the observations is large and comparable to the number of realizations of each random effect, we show that the empirical spectra of such estimators are well approximated by deterministic laws. The Stieltjes transforms of these laws are characterized by systems of fixed-point equations, which are numerically solvable by a simple iterative procedure. Our proof uses operator-valued free probability theory, and we establish a general asymptotic freeness result for families of rectangular orthogonally invariant random matrices, which is of independent interest. Our work is motivated in part by the estimation of components of covariance between multiple phenotypic traits in quantitative genetics, and we specialize our results to common experimental designs that arise in this application.

Didier Chételat, Martin T. Wells.

Source: The Annals of Statistics, Volume 47, Number 5, 2639--2670.

Abstract:
We study the behavior of a real $p$-dimensional Wishart random matrix with $n$ degrees of freedom when $n,p ightarrowinfty$ but $p/n ightarrow0$. We establish the existence of phase transitions when $p$ grows at the order $n^{(K+1)/(K+3)}$ for every $Kinmathbb{N}$, and derive expressions for approximating densities between every two phase transitions. To do this, we make use of a novel tool we call the $mathcal{F}$-conjugate of an absolutely continuous distribution, which is obtained from the Fourier transform of the square root of its density. In the case of the normalized Wishart distribution, this represents an extension of the $t$-distribution to the space of real symmetric matrices.

Qian Qin, James P. Hobert.

Source: The Annals of Statistics, Volume 47, Number 4, 2320--2347.

Abstract:
The use of MCMC algorithms in high dimensional Bayesian problems has become routine. This has spurred so-called convergence complexity analysis, the goal of which is to ascertain how the convergence rate of a Monte Carlo Markov chain scales with sample size, $n$, and/or number of covariates, $p$. This article provides a thorough convergence complexity analysis of Albert and Chib’s [ J. Amer. Statist. Assoc. 88 (1993) 669–679] data augmentation algorithm for the Bayesian probit regression model. The main tools used in this analysis are drift and minorization conditions. The usual pitfalls associated with this type of analysis are avoided by utilizing centered drift functions, which are minimized in high posterior probability regions, and by using a new technique to suppress high-dimensionality in the construction of minorization conditions. The main result is that the geometric convergence rate of the underlying Markov chain is bounded below 1 both as $n ightarrowinfty$ (with $p$ fixed), and as $p ightarrowinfty$ (with $n$ fixed). Furthermore, the first computable bounds on the total variation distance to stationarity are byproducts of the asymptotic analysis.

Mathieu Gerber, Nicolas Chopin, Nick Whiteley.

Source: The Annals of Statistics, Volume 47, Number 4, 2236--2260.

Abstract:
We study convergence and convergence rates for resampling schemes. Our first main result is a general consistency theorem based on the notion of negative association, which is applied to establish the almost sure weak convergence of measures output from Kitagawa’s [ J. Comput. Graph. Statist. 5 (1996) 1–25] stratified resampling method. Carpenter, Ckiffird and Fearnhead’s [ IEE Proc. Radar Sonar Navig. 146 (1999) 2–7] systematic resampling method is similar in structure but can fail to converge depending on the order of the input samples. We introduce a new resampling algorithm based on a stochastic rounding technique of [In 42nd IEEE Symposium on Foundations of Computer Science ( Las Vegas , NV , 2001) (2001) 588–597 IEEE Computer Soc.], which shares some attractive properties of systematic resampling, but which exhibits negative association and, therefore, converges irrespective of the order of the input samples. We confirm a conjecture made by [ J. Comput. Graph. Statist. 5 (1996) 1–25] that ordering input samples by their states in $mathbb{R}$ yields a faster rate of convergence; we establish that when particles are ordered using the Hilbert curve in $mathbb{R}^{d}$, the variance of the resampling error is ${scriptstylemathcal{O}}(N^{-(1+1/d)})$ under mild conditions, where $N$ is the number of particles. We use these results to establish asymptotic properties of particle algorithms based on resampling schemes that differ from multinomial resampling.

Yuxin Chen, Jianqing Fan, Cong Ma, Kaizheng Wang.

Source: The Annals of Statistics, Volume 47, Number 4, 2204--2235.

Abstract:
This paper is concerned with the problem of top-$K$ ranking from pairwise comparisons. Given a collection of $n$ items and a few pairwise comparisons across them, one wishes to identify the set of $K$ items that receive the highest ranks. To tackle this problem, we adopt the logistic parametric model—the Bradley–Terry–Luce model, where each item is assigned a latent preference score, and where the outcome of each pairwise comparison depends solely on the relative scores of the two items involved. Recent works have made significant progress toward characterizing the performance (e.g., the mean square error for estimating the scores) of several classical methods, including the spectral method and the maximum likelihood estimator (MLE). However, where they stand regarding top-$K$ ranking remains unsettled. We demonstrate that under a natural random sampling model, the spectral method alone, or the regularized MLE alone, is minimax optimal in terms of the sample complexity—the number of paired comparisons needed to ensure exact top-$K$ identification, for the fixed dynamic range regime. This is accomplished via optimal control of the entrywise error of the score estimates. We complement our theoretical studies by numerical experiments, confirming that both methods yield low entrywise errors for estimating the underlying scores. Our theory is established via a novel leave-one-out trick, which proves effective for analyzing both iterative and noniterative procedures. Along the way, we derive an elementary eigenvector perturbation bound for probability transition matrices, which parallels the Davis–Kahan $mathop{mathrm{sin}} olimits Theta $ theorem for symmetric matrices. This also allows us to close the gap between the $ell_{2}$ error upper bound for the spectral method and the minimax lower limit.

James G. Scott, James O. Berger

Source: Ann. Statist., Volume 38, Number 5, 2587--2619.

Abstract:
This paper studies the multiplicity-correction effect of standard Bayesian variable-selection priors in linear regression. Our first goal is to clarify when, and how, multiplicity correction happens automatically in Bayesian analysis, and to distinguish this correction from the Bayesian Ockham’s-razor effect. Our second goal is to contrast empirical-Bayes and fully Bayesian approaches to variable selection through examples, theoretical results and simulations. Considerable differences between the two approaches are found. In particular, we prove a theorem that characterizes a surprising aymptotic discrepancy between fully Bayes and empirical Bayes. This discrepancy arises from a different source than the failure to account for hyperparameter uncertainty in the empirical-Bayes estimate. Indeed, even at the extreme, when the empirical-Bayes estimate converges asymptotically to the true variable-inclusion probability, the potential for a serious difference remains.

Pooled computer resources. Grid computing, or simply grid, is the generic term given to techniques and technologies designed to make pools of distributed computer resources available on-demand. Grid computing was originally conceived by research scientists as a way of combining computers across a network to form a distributed supercomputer to tackle complex computations. In the commercial world, grid aims to maximize the utilization of an organization's computing resources by making them shareable across applications (sometimes called virtualization) and, potentially, provide computing on demand to third parties as a utility service. When used with specifications such as WSRF and WS-Notification, grid resources can appear as web services within a service-oriented architecture.

Breaking down into interchangeable pieces. For many years, software innovators have been trying to make software more like computer hardware, which is assembled from cheap, mass-produced components that connect together using standard interfaces. Component-based development (CBD) uses this approach to assemble software from reusable components within frameworks such as CORBA, Sun's Enterprise Java Beans (EJBs) and Microsoft COM. Today's service oriented architectures, based on web services, go a step further by encapsulating components in a standards-based service interface, which allows components to be reused outside their native framework. Componentization is not limited to software; through the use of subcontracting and outsourcing, it can also apply to business organizations and processes.

Boyu Ren, Sergio Bacallado, Stefano Favaro, Tommi Vatanen, Curtis Huttenhower, Lorenzo Trippa.

Source: The Annals of Applied Statistics, Volume 14, Number 1, 494--517.

Abstract:
Detecting associations between microbial compositions and sample characteristics is one of the most important tasks in microbiome studies. Most of the existing methods apply univariate models to single microbial species separately, with adjustments for multiple hypothesis testing. We propose a Bayesian analysis for a generalized mixed effects linear model tailored to this application. The marginal prior on each microbial composition is a Dirichlet process, and dependence across compositions is induced through a linear combination of individual covariates, such as disease biomarkers or the subject’s age, and latent factors. The latent factors capture residual variability and their dimensionality is learned from the data in a fully Bayesian procedure. The proposed model is tested in data analyses and simulation studies with zero-inflated compositions. In these settings and within each sample, a large proportion of counts per microbial species are equal to zero. In our Bayesian model a priori the probability of compositions with absent microbial species is strictly positive. We propose an efficient algorithm to sample from the posterior and visualizations of model parameters which reveal associations between covariates and microbial compositions. We evaluate the proposed method in simulation studies, and then analyze a microbiome dataset for infants with type 1 diabetes which contains a large proportion of zeros in the sample-specific microbial compositions.

Zhonghua Liu, Ian Barnett, Xihong Lin.

Source: The Annals of Applied Statistics, Volume 14, Number 1, 433--451.

Abstract:
Principal component analysis (PCA) is a popular method for dimension reduction in unsupervised multivariate analysis. However, existing ad hoc uses of PCA in both multivariate regression (multiple outcomes) and multiple regression (multiple predictors) lack theoretical justification. The differences in the statistical properties of PCAs in these two regression settings are not well understood. In this paper we provide theoretical results on the power of PCA in genetic association testings in both multiple phenotype and SNP-set settings. The multiple phenotype setting refers to the case when one is interested in studying the association between a single SNP and multiple phenotypes as outcomes. The SNP-set setting refers to the case when one is interested in studying the association between multiple SNPs in a SNP set and a single phenotype as the outcome. We demonstrate analytically that the properties of the PC-based analysis in these two regression settings are substantially different. We show that the lower order PCs, that is, PCs with large eigenvalues, are generally preferred and lead to a higher power in the SNP-set setting, while the higher-order PCs, that is, PCs with small eigenvalues, are generally preferred in the multiple phenotype setting. We also investigate the power of three other popular statistical methods, the Wald test, the variance component test and the minimum $p$-value test, in both multiple phenotype and SNP-set settings. We use theoretical power, simulation studies, and two real data analyses to validate our findings.

Peng Shi, Zifeng Zhao.

Source: The Annals of Applied Statistics, Volume 14, Number 1, 357--380.

Abstract:
In actuarial research a task of particular interest and importance is to predict the loss cost for individual risks so that informative decisions are made in various insurance operations such as underwriting, ratemaking and capital management. The loss cost is typically viewed to follow a compound distribution where the summation of the severity variables is stopped by the frequency variable. A challenging issue in modeling such outcomes is to accommodate the potential dependence between the number of claims and the size of each individual claim. In this article we introduce a novel regression framework for compound distributions that uses a copula to accommodate the association between the frequency and the severity variables and, thus, allows for arbitrary dependence between the two components. We further show that the new model is very flexible and is easily modified to account for incomplete data due to censoring or truncation. The flexibility of the proposed model is illustrated using both simulated and real data sets. In the analysis of granular claims data from property insurance, we find substantive negative relationship between the number and the size of insurance claims. In addition, we demonstrate that ignoring the frequency-severity association could lead to biased decision-making in insurance operations.

Hong Zhang, Tiejun Tong, John Landers, Zheyang Wu.

Source: The Annals of Applied Statistics, Volume 14, Number 1, 178--201.

Abstract:
The $p$-value combination approach is an important statistical strategy for testing global hypotheses with broad applications in signal detection, meta-analysis, data integration, etc. In this paper we extend the classic Fisher’s combination method to a unified family of statistics, called TFisher, which allows a general truncation-and-weighting scheme of input $p$-values. TFisher can significantly improve statistical power over the Fisher and related truncation-only methods for detecting both rare and dense “signals.” To address wide applications, analytical calculations for TFisher’s size and power are deduced under any two continuous distributions in the null and the alternative hypotheses. The corresponding omnibus test (oTFisher) and its size calculation are also provided for data-adaptive analysis. We study the asymptotic optimal parameters of truncation and weighting based on Bahadur efficiency (BE). A new asymptotic measure, called the asymptotic power efficiency (APE), is also proposed for better reflecting the statistics’ performance in real data analysis. Interestingly, under the Gaussian mixture model in the signal detection problem, both BE and APE indicate that the soft-thresholding scheme is the best, the truncation and weighting parameters should be equal. By simulations of various signal patterns, we systematically compare the power of statistics within TFisher family as well as some rare-signal-optimal tests. We illustrate the use of TFisher in an exome-sequencing analysis for detecting novel genes of amyotrophic lateral sclerosis. Relevant computation has been implemented into an R package TFisher published on the Comprehensive R Archive Network to cater for applications.

Zhenguo Gao, Pang Du, Ran Jin, John L. Robertson.

Source: The Annals of Applied Statistics, Volume 14, Number 1, 143--159.

Abstract:
Liver procurement experiments with surface-temperature monitoring motivated Gao et al. ( J. Amer. Statist. Assoc. 114 (2019) 773–781) to develop a variance change-point detection method under a smoothly-changing mean trend. However, the spotwise change points yielded from their method do not offer immediate information to surgeons since an organ is often transplanted as a whole or in part. We develop a new practical method that can analyze a defined portion of the organ surface at a time. It also provides a novel addition to the developing field of functional data monitoring. Furthermore, numerical challenge emerges for simultaneously modeling the variance functions of 2D locations and the mean function of location and time. The respective sample sizes in the scales of 10,000 and 1,000,000 for modeling these functions make standard spline estimation too costly to be useful. We introduce a multistage subsampling strategy with steps educated by quickly-computable preliminary statistical measures. Extensive simulations show that the new method can efficiently reduce the computational cost and provide reasonable parameter estimates. Application of the new method to our liver surface temperature monitoring data shows its effectiveness in providing accurate status change information for a selected portion of the organ in the experiment.

Francisco J. R. Ruiz, Susan Athey, David M. Blei.

Source: The Annals of Applied Statistics, Volume 14, Number 1, 1--27.

Abstract:
We develop SHOPPER, a sequential probabilistic model of shopping data. SHOPPER uses interpretable components to model the forces that drive how a customer chooses products; in particular, we designed SHOPPER to capture how items interact with other items. We develop an efficient posterior inference algorithm to estimate these forces from large-scale data, and we analyze a large dataset from a major chain grocery store. We are interested in answering counterfactual queries about changes in prices. We found that SHOPPER provides accurate predictions even under price interventions, and that it helps identify complementary and substitutable pairs of products.

Joe Watson, James V. Zidek, Gavin Shaddick.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2662--2700.

Abstract:
This paper presents a general model framework for detecting the preferential sampling of environmental monitors recording an environmental process across space and/or time. This is achieved by considering the joint distribution of an environmental process with a site-selection process that considers where and when sites are placed to measure the process. The environmental process may be spatial, temporal or spatio-temporal in nature. By sharing random effects between the two processes, the joint model is able to establish whether site placement was stochastically dependent of the environmental process under study. Furthermore, if stochastic dependence is identified between the two processes, then inferences about the probability distribution of the spatio-temporal process will change, as will predictions made of the process across space and time. The embedding into a spatio-temporal framework also allows for the modelling of the dynamic site-selection process itself. Real-world factors affecting both the size and location of the network can be easily modelled and quantified. Depending upon the choice of the population of locations considered for selection across space and time under the site-selection process, different insights about the precise nature of preferential sampling can be obtained. The general framework developed in the paper is designed to be easily and quickly fit using the R-INLA package. We apply this framework to a case study involving particulate air pollution over the UK where a major reduction in the size of a monitoring network through time occurred. It is demonstrated that a significant response-biased reduction in the air quality monitoring network occurred, namely the relocation of monitoring sites to locations with the highest pollution levels, and the routine removal of sites at locations with the lowest. We also show that the network was consistently unrepresenting levels of particulate matter seen across much of GB throughout the operating life of the network. Finally we show that this may have led to a severe overreporting of the population-average exposure levels experienced across GB. This could have great impacts on estimates of the health effects of black smoke levels.

Elizabeth Lorenzi, Ricardo Henao, Katherine Heller.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2637--2661.

Abstract:
Nearly a third of all surgeries performed in the United States occur for patients over the age of 65; these older adults experience a higher rate of postoperative morbidity and mortality. To improve the care for these patients, we aim to identify and characterize high risk geriatric patients to send to a specialized perioperative clinic while leveraging the overall surgical population to improve learning. To this end, we develop a hierarchical infinite latent factor model (HIFM) to appropriately account for the covariance structure across subpopulations in data. We propose a novel Hierarchical Dirichlet Process shrinkage prior on the loadings matrix that flexibly captures the underlying structure of our data while sharing information across subpopulations to improve inference and prediction. The stick-breaking construction of the prior assumes an infinite number of factors and allows for each subpopulation to utilize different subsets of the factor space and select the number of factors needed to best explain the variation. We develop the model into a latent factor regression method that excels at prediction and inference of regression coefficients. Simulations validate this strong performance compared to baseline methods. We apply this work to the problem of predicting surgical complications using electronic health record data for geriatric patients and all surgical patients at Duke University Health System (DUHS). The motivating application demonstrates the improved predictive performance when using HIFM in both area under the ROC curve and area under the PR Curve while providing interpretable coefficients that may lead to actionable interventions.

Silvia Metelli, Nicholas Heard.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2586--2610.

Abstract:
Monitoring computer network traffic for anomalous behaviour presents an important security challenge. Arrivals of new edges in a network graph represent connections between a client and server pair not previously observed, and in rare cases these might suggest the presence of intruders or malicious implants. We propose a Bayesian model and anomaly detection method for simultaneously characterising existing network structure and modelling likely new edge formation. The method is demonstrated on real computer network authentication data and successfully identifies some machines which are known to be compromised.

Seth Flaxman, Michael Chirico, Pau Pereira, Charles Loeffler.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2564--2585.

Abstract:
We propose a generic spatiotemporal event forecasting method which we developed for the National Institute of Justice’s (NIJ) Real-Time Crime Forecasting Challenge (National Institute of Justice (2017)). Our method is a spatiotemporal forecasting model combining scalable randomized Reproducing Kernel Hilbert Space (RKHS) methods for approximating Gaussian processes with autoregressive smoothing kernels in a regularized supervised learning framework. While the smoothing kernels capture the two main approaches in current use in the field of crime forecasting, kernel density estimation (KDE) and self-exciting point process (SEPP) models, the RKHS component of the model can be understood as an approximation to the popular log-Gaussian Cox Process model. For inference, we discretize the spatiotemporal point pattern and learn a log-intensity function using the Poisson likelihood and highly efficient gradient-based optimization methods. Model hyperparameters including quality of RKHS approximation, spatial and temporal kernel lengthscales, number of autoregressive lags and bandwidths for smoothing kernels as well as cell shape, size and rotation, were learned using cross validation. Resulting predictions significantly exceeded baseline KDE estimates and SEPP models for sparse events.

Armin Schwartzman, Andrew J. Schork, Rong Zablocki, Wesley K. Thompson.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2509--2538.

Abstract:
Analysis of genome-wide association studies (GWAS) is characterized by a large number of univariate regressions where a quantitative trait is regressed on hundreds of thousands to millions of single-nucleotide polymorphism (SNP) allele counts, one at a time. This article proposes an estimator of the SNP heritability of the trait, defined here as the fraction of the variance of the trait explained by the SNPs in the study. The proposed GWAS heritability (GWASH) estimator is easy to compute, highly interpretable and is consistent as the number of SNPs and the sample size increase. More importantly, it can be computed from summary statistics typically reported in GWAS, not requiring access to the original data. The estimator takes full account of the linkage disequilibrium (LD) or correlation between the SNPs in the study through moments of the LD matrix, estimable from auxiliary datasets. Unlike other proposed estimators in the literature, we establish the theoretical properties of the GWASH estimator and obtain analytical estimates of the precision, allowing for power and sample size calculations for SNP heritability estimates and forming a firm foundation for future methodological development.

Kun Liang.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2452--2482.

Abstract:
Finding differentially expressed genes is a common task in high-throughput transcriptome studies. While traditional statistical methods rank the genes by their test statistics alone, we analyze an RNA sequencing dataset using the auxiliary information of gene length and the test statistics from a related microarray study. Given the auxiliary information, we propose a novel nonparametric empirical Bayes procedure to estimate the posterior probability of differential expression for each gene. We demonstrate the advantage of our procedure in extensive simulation studies and a psoriasis RNA sequencing study. The companion R package calm is available at Bioconductor.