England : National Association for Maternal and Child Welfare, 1961.

Stuttgart : Franz Steiner Verlag, 2019.

Stuttgart : In Kommission: Wissenschaftliche Verlagsgesellschaft mbH, 2019.

Rockville, Maryland : The National Institute on Drug Abuse, 1976.

[London] : [publisher not identified], [2019]

Washington, D.C. : Department of Transportation, Federal Railroad Administration, 1976.

Washington, D.C. : Wynne Associates, 1974.

Sabrina Ionescu wins the Wooden Award for the second year in a row, becoming the fifth in the trophy's history to win in back-to-back seasons. With the honor, she completes a complete sweep of the national postseason player of the year awards. As a senior, Ionescu matched her own single-season mark with eight triple-doubles in 2019-20, and she was incredibly efficient from the field with a career-best 51.8 field goal percentage.

For Vic Schaefer, the decision to take over the Texas women's basketball program was profoundly personal. “It was a calling,” Schaefer said Monday, noting the old Austin hospital building where he was born is just across the street from where the Longhorns play at the Frank Erwin Center. Texas quickly snatched up Schaefer on Sunday, just two days after athletic director Chris Del Conte announced coach Karen Aston would not be retained after eight seasons.

Arizona's Aari McDonald and Pac-12 Networks' Ashley Adamson discuss the guard's decision to return for her senior season in Tucson and how she now has the opportunity to be the face of the league. McDonald, the Pac-12 Defensive Player of the Year, was one of the nation's top scorers in 2019-20, averaging 20.6 points per game.

Olivier Roustant, Fabrice Gamboa, Bertrand Iooss.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 386--412.

Abstract:
The so-called polynomial chaos expansion is widely used in computer experiments. For example, it is a powerful tool to estimate Sobol’ sensitivity indices. In this paper, we consider generalized chaos expansions built on general tensor Hilbert basis. In this frame, we revisit the computation of the Sobol’ indices with Parseval equalities and give general lower bounds for these indices obtained by truncation. The case of the eigenfunctions system associated with a Poincaré differential operator leads to lower bounds involving the derivatives of the analyzed function and provides an efficient tool for variable screening. These lower bounds are put in action both on toy and real life models demonstrating their accuracy.

We study the question of whether parallelization in the exploration of the feasible set can be used to speed up convex optimization, in the local oracle model of computation and in the high-dimensional regime. We show that the answer is negative for both deterministic and randomized algorithms applied to essentially any of the interesting geometries and nonsmooth, weakly-smooth, or smooth objective functions. In particular, we show that it is not possible to obtain a polylogarithmic (in the sequential complexity of the problem) number of parallel rounds with a polynomial (in the dimension) number of queries per round. In the majority of these settings and when the dimension of the space is polynomial in the inverse target accuracy, our lower bounds match the oracle complexity of sequential convex optimization, up to at most a logarithmic factor in the dimension, which makes them (nearly) tight. Another conceptual contribution of our work is in providing a general and streamlined framework for proving lower bounds in the setting of parallel convex optimization. Prior to our work, lower bounds for parallel convex optimization algorithms were only known in a small fraction of the settings considered in this paper, mainly applying to Euclidean ($ell_2$) and $ell_infty$ spaces.

We study the misclassification error for community detection in general heterogeneous stochastic block models (SBM) with noisy or partial label information. We establish a connection between the misclassification rate and the notion of minimum energy on the local neighborhood of the SBM. We develop an optimally weighted message passing algorithm to reconstruct labels for SBM based on the minimum energy flow and the eigenvectors of a certain Markov transition matrix. The general SBM considered in this paper allows for unequal-size communities, degree heterogeneity, and different connection probabilities among blocks. We focus on how to optimally weigh the message passing to improve misclassification.

We study the identity testing problem in the context of spin systems or undirected graphical models, where it takes the following form: given the parameter specification of the model $M$ and a sampling oracle for the distribution $mu_{M^*}$ of an unknown model $M^*$, can we efficiently determine if the two models $M$ and $M^*$ are the same? We consider identity testing for both soft-constraint and hard-constraint systems. In particular, we prove hardness results in two prototypical cases, the Ising model and proper colorings, and explore whether identity testing is any easier than structure learning. For the ferromagnetic (attractive) Ising model, Daskalakis et al. (2018) presented a polynomial-time algorithm for identity testing. We prove hardness results in the antiferromagnetic (repulsive) setting in the same regime of parameters where structure learning is known to require a super-polynomial number of samples. Specifically, for $n$-vertex graphs of maximum degree $d$, we prove that if $|eta| d = omega(log{n})$ (where $eta$ is the inverse temperature parameter), then there is no polynomial running time identity testing algorithm unless $RP=NP$. In the hard-constraint setting, we present hardness results for identity testing for proper colorings. Our results are based on the presumed hardness of #BIS, the problem of (approximately) counting independent sets in bipartite graphs.

Derivatives play an important role in bandwidth selection methods (e.g., plug-ins), data analysis and bias-corrected confidence intervals. Therefore, obtaining accurate derivative information is crucial. Although many derivative estimation methods exist, the majority require a fixed design assumption. In this paper, we propose an effective and fully data-driven framework to estimate the first and second order derivative in random design. We establish the asymptotic properties of the proposed derivative estimator, and also propose a fast selection method for the tuning parameters. The performance and flexibility of the method is illustrated via an extensive simulation study.

In many areas, practitioners need to analyze large data sets that challenge conventional single-machine computing. To scale up data analysis, distributed and parallel computing approaches are increasingly needed. Here we study a fundamental and highly important problem in this area: How to do ridge regression in a distributed computing environment? Ridge regression is an extremely popular method for supervised learning, and has several optimality properties, thus it is important to study. We study one-shot methods that construct weighted combinations of ridge regression estimators computed on each machine. By analyzing the mean squared error in a high-dimensional random-effects model where each predictor has a small effect, we discover several new phenomena. Infinite-worker limit: The distributed estimator works well for very large numbers of machines, a phenomenon we call 'infinite-worker limit'. Optimal weights: The optimal weights for combining local estimators sum to more than unity, due to the downward bias of ridge. Thus, all averaging methods are suboptimal. We also propose a new Weighted ONe-shot DistributEd Ridge regression algorithm (WONDER). We test WONDER in simulation studies and using the Million Song Dataset as an example. There it can save at least 100x in computation time, while nearly preserving test accuracy.

Tree data are ubiquitous because they model a large variety of situations, e.g., the architecture of plants, the secondary structure of RNA, or the hierarchy of XML files. Nevertheless, the analysis of these non-Euclidean data is difficult per se. In this paper, we focus on the subtree kernel that is a convolution kernel for tree data introduced by Vishwanathan and Smola in the early 2000's. More precisely, we investigate the influence of the weight function from a theoretical perspective and in real data applications. We establish on a 2-classes stochastic model that the performance of the subtree kernel is improved when the weight of leaves vanishes, which motivates the definition of a new weight function, learned from the data and not fixed by the user as usually done. To this end, we define a unified framework for computing the subtree kernel from ordered or unordered trees, that is particularly suitable for tuning parameters. We show through eight real data classification problems the great efficiency of our approach, in particular for small data sets, which also states the high importance of the weight function. Finally, a visualization tool of the significant features is derived.

Abedin Haidari, Amir T. Payandeh Najafabadi, Narayanaswamy Balakrishnan.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 1, 150--166.

Abstract:
Consider two parallel systems, say $A$ and $B$, with respective lifetimes $T_{1}$ and $T_{2}$ wherein independent component lifetimes of each system follow exponentiated generalized gamma distribution with possibly different exponential shape and scale parameters. We show here that $T_{2}$ is smaller than $T_{1}$ with respect to the usual stochastic order (reversed hazard rate order) if the vector of logarithm (the main vector) of scale parameters of System $B$ is weakly weighted majorized by that of System $A$, and if the vector of exponential shape parameters of System $A$ is unordered mojorized by that of System $B$. By means of some examples, we show that the above results can not be extended to the hazard rate and likelihood ratio orders. However, when the scale parameters of each system divide into two homogeneous groups, we verify that the usual stochastic and reversed hazard rate orders can be extended, respectively, to the hazard rate and likelihood ratio orders. The established results complete and strengthen some of the known results in the literature.

Abbas Pak, M. E. Ghitany, Mohammad Reza Mahmoudi.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 4, 894--914.

Abstract:
This paper focuses on Bayesian estimation of the parameters and reliability function of the power Lindley distribution by using various symmetric and asymmetric loss functions. Assuming suitable priors on the parameters, Bayes estimates are derived by using squared error, linear exponential (linex) and general entropy loss functions. Since, under these loss functions, Bayes estimates of the parameters do not have closed forms we use lindley’s approximation technique to calculate the Bayes estimates. Moreover, we obtain the Bayes estimates of the parameters using a Markov Chain Monte Carlo (MCMC) method. Simulation studies are conducted in order to evaluate the performances of the proposed estimators under the considered loss functions. Finally, analysis of a real data set is presented for illustrative purposes.

Rodrigo Citton P. dos Reis, Enrico A. Colosimo, Gustavo L. Gilardoni.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 2, 374--396.

Abstract:
In the data analysis from multiple repairable systems, it is usual to observe both different truncation times and heterogeneity among the systems. Among other reasons, the latter is caused by different manufacturing lines and maintenance teams of the systems. In this paper, a hierarchical model is proposed for the statistical analysis of multiple repairable systems under different truncation times. A reparameterization of the power law process is proposed in order to obtain a quasi-conjugate bayesian analysis. An empirical Bayes approach is used to estimate model hyperparameters. The uncertainty in the estimate of these quantities are corrected by using a parametric bootstrap approach. The results are illustrated in a real data set of failure times of power transformers from an electric company in Brazil.

Solveig Engebretsen, Ingrid K. Glad.

Source: Statistics Surveys, Volume 13, 1--51.

Abstract:
In numerous problems where the aim is to estimate the effect of a predictor variable on a response, one can assume a monotone relationship. For example, dose-effect models in medicine are of this type. In a multiple regression setting, additive monotone regression models assume that each predictor has a monotone effect on the response. In this paper, we present an overview and comparison of very recent frequentist methods for fitting additive monotone regression models. Three of the methods we present can be used both in the high dimensional setting, where the number of parameters $p$ exceeds the number of observations $n$, and in the classical multiple setting where $1<pleq n$. However, many of the most recent methods only apply to the classical setting. The methods are compared through simulation experiments in terms of efficiency, prediction error and variable selection properties in both settings, and they are applied to the Boston housing data. We conclude with some recommendations on when the various methods perform best.

The transfer learning technique is widely used to learning in one context and applying it to another, i.e. the capacity to apply acquired knowledge and skills to new situations. But is it possible to transfer the learning from a deep neural network to a weaker neural network? Is it possible to improve the performance of a weak neural network using the knowledge acquired by a more powerful neural network? In this work, during the training process of a weak network, we add a loss function that minimizes the distance between the features previously learned from a strong neural network with the features that the weak network must try to learn. To demonstrate the effectiveness and robustness of our approach, we conducted a large number of experiments using three known datasets and demonstrated that a weak neural network can increase its performance if its learning process is driven by a more powerful neural network.

Boosting is one of the most successful ideas in machine learning. The most well-accepted explanations for the low generalization error of boosting algorithms such as AdaBoost stem from margin theory. The study of margins in the context of boosting algorithms was initiated by Schapire, Freund, Bartlett and Lee (1998) and has inspired numerous boosting algorithms and generalization bounds. To date, the strongest known generalization (upper bound) is the $k$th margin bound of Gao and Zhou (2013). Despite the numerous generalization upper bounds that have been proved over the last two decades, nothing is known about the tightness of these bounds. In this paper, we give the first margin-based lower bounds on the generalization error of boosted classifiers. Our lower bounds nearly match the $k$th margin bound and thus almost settle the generalization performance of boosted classifiers in terms of margins.

The $p$-tensor Curie-Weiss model is a two-parameter discrete exponential family for modeling dependent binary data, where the sufficient statistic has a linear term and a term with degree $p geq 2$. This is a special case of the tensor Ising model and the natural generalization of the matrix Curie-Weiss model, which provides a convenient mathematical abstraction for capturing, not just pairwise, but higher-order dependencies. In this paper we provide a complete description of the limiting properties of the maximum likelihood (ML) estimates of the natural parameters, given a single sample from the $p$-tensor Curie-Weiss model, for $p geq 3$, complementing the well-known results in the matrix ($p=2$) case (Comets and Gidas (1991)). Our results unearth various new phase transitions and surprising limit theorems, such as the existence of a 'critical' curve in the parameter space, where the limiting distribution of the ML estimates is a mixture with both continuous and discrete components. The number of mixture components is either two or three, depending on, among other things, the sign of one of the parameters and the parity of $p$. Another interesting revelation is the existence of certain 'special' points in the parameter space where the ML estimates exhibit a superefficiency phenomenon, converging to a non-Gaussian limiting distribution at rate $N^{frac{3}{4}}$. We discuss how these results can be used to construct confidence intervals for the model parameters and, as a byproduct of our analysis, obtain limit theorems for the sample mean, which provide key insights into the statistical properties of the model.

The ability of intelligent agents to learn and remember multiple tasks sequentially is crucial to achieving artificial general intelligence. Many continual learning (CL) methods have been proposed to overcome catastrophic forgetting. Catastrophic forgetting notoriously impedes the sequential learning of neural networks as the data of previous tasks are unavailable. In this paper we focus on class incremental learning, a challenging CL scenario, in which classes of each task are disjoint and task identity is unknown during test. For this scenario, generative replay is an effective strategy which generates and replays pseudo data for previous tasks to alleviate catastrophic forgetting. However, it is not trivial to learn a generative model continually for relatively complex data. Based on recently proposed orthogonal weight modification (OWM) algorithm which can keep previously learned input-output mappings invariant approximately when learning new tasks, we propose to directly generate and replay feature. Empirical results on image and text datasets show our method can improve OWM consistently by a significant margin while conventional generative replay always results in a negative effect. Our method also beats a state-of-the-art generative replay method and is competitive with a strong baseline based on real data storage.

In the variational relevance vector machine, the gamma distribution is representative as a hyperprior over the noise precision of automatic relevance determination prior. Instead of the gamma hyperprior, we propose to use the inverse gamma hyperprior with a shape parameter close to zero and a scale parameter not necessary close to zero. This hyperprior is associated with the concept of a weakly informative prior. The effect of this hyperprior is investigated through regression to non-homogeneous data. Because it is difficult to capture the structure of such data with a single kernel function, we apply the multiple kernel method, in which multiple kernel functions with different widths are arranged for input data. We confirm that the degrees of freedom in a model is controlled by adjusting the scale parameter and keeping the shape parameter close to zero. A candidate for selecting the scale parameter is the predictive information criterion. However the estimated model using this criterion seems to cause over-fitting. This is because the multiple kernel method makes the model a situation where the dimension of the model is larger than the data size. To select an appropriate scale parameter even in such a situation, we also propose an extended prediction information criterion. It is confirmed that a multiple kernel relevance vector regression model with good predictive accuracy can be obtained by selecting the scale parameter minimizing extended prediction information criterion.

We present SmartExchange, an algorithm-hardware co-design framework to trade higher-cost memory storage/access for lower-cost computation, for energy-efficient inference of deep neural networks (DNNs). We develop a novel algorithm to enforce a specially favorable DNN weight structure, where each layerwise weight matrix can be stored as the product of a small basis matrix and a large sparse coefficient matrix whose non-zero elements are all power-of-2. To our best knowledge, this algorithm is the first formulation that integrates three mainstream model compression ideas: sparsification or pruning, decomposition, and quantization, into one unified framework. The resulting sparse and readily-quantized DNN thus enjoys greatly reduced energy consumption in data movement as well as weight storage. On top of that, we further design a dedicated accelerator to fully utilize the SmartExchange-enforced weights to improve both energy efficiency and latency performance. Extensive experiments show that 1) on the algorithm level, SmartExchange outperforms state-of-the-art compression techniques, including merely sparsification or pruning, decomposition, and quantization, in various ablation studies based on nine DNN models and four datasets; and 2) on the hardware level, the proposed SmartExchange based accelerator can improve the energy efficiency by up to 6.7$ imes$ and the speedup by up to 19.2$ imes$ over four state-of-the-art DNN accelerators, when benchmarked on seven DNN models (including four standard DNNs, two compact DNN models, and one segmentation model) and three datasets.

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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.

Min Xu, Varun Jog, Po-Ling Loh.

Source: The Annals of Statistics, Volume 48, Number 1, 183--204.

Abstract:
Community identification in a network is an important problem in fields such as social science, neuroscience and genetics. Over the past decade, stochastic block models (SBMs) have emerged as a popular statistical framework for this problem. However, SBMs have an important limitation in that they are suited only for networks with unweighted edges; in various scientific applications, disregarding the edge weights may result in a loss of valuable information. We study a weighted generalization of the SBM, in which observations are collected in the form of a weighted adjacency matrix and the weight of each edge is generated independently from an unknown probability density determined by the community membership of its endpoints. We characterize the optimal rate of misclustering error of the weighted SBM in terms of the Renyi divergence of order 1/2 between the weight distributions of within-community and between-community edges, substantially generalizing existing results for unweighted SBMs. Furthermore, we present a computationally tractable algorithm based on discretization that achieves the optimal error rate. Our method is adaptive in the sense that the algorithm, without assuming knowledge of the weight densities, performs as well as the best algorithm that knows the weight densities.

Aryeh Kontorovich, Iosif Pinelis.

Source: The Annals of Statistics, Volume 47, Number 5, 2822--2854.

Abstract:
We provide an exact nonasymptotic lower bound on the minimax expected excess risk (EER) in the agnostic probably-approximately-correct (PAC) machine learning classification model and identify minimax learning algorithms as certain maximally symmetric and minimally randomized “voting” procedures. Based on this result, an exact asymptotic lower bound on the minimax EER is provided. This bound is of the simple form $c_{infty}/sqrt{ u}$ as $ u oinfty$, where $c_{infty}=0.16997dots$ is a universal constant, $ u=m/d$, $m$ is the size of the training sample and $d$ is the Vapnik–Chervonenkis dimension of the hypothesis class. It is shown that the differences between these asymptotic and nonasymptotic bounds, as well as the differences between these two bounds and the maximum EER of any learning algorithms that minimize the empirical risk, are asymptotically negligible, and all these differences are due to ties in the mentioned “voting” procedures. A few easy to compute nonasymptotic lower bounds on the minimax EER are also obtained, which are shown to be close to the exact asymptotic lower bound $c_{infty}/sqrt{ u}$ even for rather small values of the ratio $ u=m/d$. As an application of these results, we substantially improve existing lower bounds on the tail probability of the excess risk. Among the tools used are Bayes estimation and apparently new identities and inequalities for binomial distributions.

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.

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.

Arnab Chakraborty, Soumendra Nath Lahiri, Alyson Wilson.

Source: The Annals of Applied Statistics, Volume 14, Number 1, 116--142.

Abstract:
Spatial prediction of weather elements like temperature, precipitation, and barometric pressure are generally based on satellite imagery or data collected at ground stations. None of these data provide information at a more granular or “hyperlocal” resolution. On the other hand, crowdsourced weather data, which are captured by sensors installed on mobile devices and gathered by weather-related mobile apps like WeatherSignal and AccuWeather, can serve as potential data sources for analyzing environmental processes at a hyperlocal resolution. However, due to the low quality of the sensors and the nonlaboratory environment, the quality of the observations in crowdsourced data is compromised. This paper describes methods to improve hyperlocal spatial prediction using this varying-quality, noisy crowdsourced information. We introduce a reliability metric, namely Veracity Score (VS), to assess the quality of the crowdsourced observations using a coarser, but high-quality, reference data. A VS-based methodology to analyze noisy spatial data is proposed and evaluated through extensive simulations. The merits of the proposed approach are illustrated through case studies analyzing crowdsourced daily average ambient temperature readings for one day in the contiguous United States.

Fan Li, Fan Li.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2389--2415.

Abstract:
Causal or unconfounded descriptive comparisons between multiple groups are common in observational studies. Motivated from a racial disparity study in health services research, we propose a unified propensity score weighting framework, the balancing weights, for estimating causal effects with multiple treatments. These weights incorporate the generalized propensity scores to balance the weighted covariate distribution of each treatment group, all weighted toward a common prespecified target population. The class of balancing weights include several existing approaches such as the inverse probability weights and trimming weights as special cases. Within this framework, we propose a set of target estimands based on linear contrasts. We further develop the generalized overlap weights, constructed as the product of the inverse probability weights and the harmonic mean of the generalized propensity scores. The generalized overlap weighting scheme corresponds to the target population with the most overlap in covariates across the multiple treatments. These weights are bounded and thus bypass the problem of extreme propensities. We show that the generalized overlap weights minimize the total asymptotic variance of the moment weighting estimators for the pairwise contrasts within the class of balancing weights. We consider two balance check criteria and propose a new sandwich variance estimator for estimating the causal effects with generalized overlap weights. We apply these methods to study the racial disparities in medical expenditure between several racial groups using the 2009 Medical Expenditure Panel Survey (MEPS) data. Simulations were carried out to compare with existing methods.

Chanmin Kim, Michael J. Daniels, Joseph W. Hogan, Christine Choirat, Corwin M. Zigler.

Source: The Annals of Applied Statistics, Volume 13, Number 3, 1927--1956.

Abstract:
Emission control technologies installed on power plants are a key feature of many air pollution regulations in the US. While such regulations are predicated on the presumed relationships between emissions, ambient air pollution and human health, many of these relationships have never been empirically verified. The goal of this paper is to develop new statistical methods to quantify these relationships. We frame this problem as one of mediation analysis to evaluate the extent to which the effect of a particular control technology on ambient pollution is mediated through causal effects on power plant emissions. Since power plants emit various compounds that contribute to ambient pollution, we develop new methods for multiple intermediate variables that are measured contemporaneously, may interact with one another, and may exhibit joint mediating effects. Specifically, we propose new methods leveraging two related frameworks for causal inference in the presence of mediating variables: principal stratification and causal mediation analysis. We define principal effects based on multiple mediators, and also introduce a new decomposition of the total effect of an intervention on ambient pollution into the natural direct effect and natural indirect effects for all combinations of mediators. Both approaches are anchored to the same observed-data models, which we specify with Bayesian nonparametric techniques. We provide assumptions for estimating principal causal effects, then augment these with an additional assumption required for causal mediation analysis. The two analyses, interpreted in tandem, provide the first empirical investigation of the presumed causal pathways that motivate important air quality regulatory policies.

Pavel Zorin-Kranich.

Source: Bernoulli, Volume 26, Number 3, 2311--2318.

Abstract:
We prove an estimate for weighted $p$th moments of the pathwise $r$-variation of a martingale in terms of the $A_{p}$ characteristic of the weight. The novelty of the proof is that we avoid real interpolation techniques.