InBios International, Inc. announces the U.S. Food and Drug Administration (FDA) issued an emergency use authorization (EUA) for its diagnostic test that can be used immediately by CLIA...

(PRWeb April 08, 2020)

Read the full story at https://www.prweb.com/releases/inbios_receives_emergency_use_authorization_for_its_smart_detect_sars_cov_2_rrt_pcr_kit_for_detection_of_the_virus_causing_covid_19/prweb17036897.htm

Hays County announced it has joined the Texas Purchasing Group and will be publishing and distributing upcoming bid opportunities on the system along with their current platform in these unprecedented...

(PRWeb April 09, 2020)

Read the full story at https://www.prweb.com/releases/hays_county_joins_the_texas_purchasing_group_by_bidnet_direct/prweb17021429.htm

According to data released by Power to Decide, an estimated 369,960 New Jersey women of reproductive age (13-44) in need of publicly funded contraception live in counties impacted by the...

(PRWeb April 09, 2020)

Read the full story at https://www.prweb.com/releases/domestic_gag_rule_reduces_contraceptive_access_for_nearly_370_000_women_living_in_new_jersey/prweb17040987.htm

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

(PRWeb April 15, 2020)

Read the full story at https://www.prweb.com/releases/wine_retailers_seek_alcohol_shipping_compromise_with_18_states/prweb17050617.htm

Harvested produce crops feed Florida Department of Corrections’ (FDC) more than 87,000 inmates; action saves food costs while reducing COVID-19 related supply chain impacts.

(PRWeb April 20, 2020)

Read the full story at https://www.prweb.com/releases/new_partnerships_emerge_for_covid_19_relief_dade_county_farm_bureau_teams_with_state_leaders_to_launch_farm_to_inmate_program/prweb17052045.htm

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)

Read the full story at https://www.prweb.com/releases/gun_rights_california_gun_owners_ammo_dealers_fire_back_against_proposition_63/prweb17075447.htm

In a public-private partnership to develop housing, resident services and hope for 102 working families in Haster Orangewood community, Jamboree Housing Corporation and the City of Anaheim announce...

(PRWeb April 27, 2020)

Read the full story at https://www.prweb.com/releases/jamboree_begins_construction_on_capstone_development_to_change_trajectory_of_neighborhood_in_anaheim_ca/prweb17073166.htm

The drones and programs will be fully paid for by the DOJ as part of the $850 million funding that has been allocated to help public safety departments fight the spread of COVID-19. This includes...

(PRWeb April 30, 2020)

Read the full story at https://www.prweb.com/releases/suntuity_airworks_offering_free_assistance_in_drone_acquisition_through_850mm_federal_grant_assistance_program_for_public_safety_agencies/prweb17090555.htm

With New York is on PAUSE, the Alliance of New York State YMCAs will showcase how YMCAs are staying “Open For Good” to meet the needs of their community during the COVID-19 crisis on Giving Tuesday...

(PRWeb May 02, 2020)

Read the full story at https://www.prweb.com/releases/new_york_state_ymcas_are_open_for_good/prweb17088694.htm

PMA, a premier full-service provider of comprehensive financial and investment advisory services to municipalities, school districts, local government pools, insurance companies and other...

(PRWeb May 04, 2020)

Read the full story at https://www.prweb.com/releases/pma_reveals_new_logo_and_brand_identity/prweb17090459.htm

Newly launched REBA Institute shares research suggesting multiple policy pathways increase access, lower costs and drive decarbonization of the electricity sector.

(PRWeb May 05, 2020)

Read the full story at https://www.prweb.com/releases/viable_policy_pathways_expand_access_to_renewable_energy_for_commercial_industrial_sector/prweb17099869.htm

Defendant’s Motion to Exclude Expert Testimony regarding evidence generated by STRmix denied.

(PRWeb May 08, 2020)

Read the full story at https://www.prweb.com/releases/colorado_court_rules_strmix_is_relevant_and_reliable_practice_for_interpreting_likelihood_ratios/prweb17101548.htm

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.

Gregory Cox.

Source: The Annals of Statistics, Volume 48, Number 1, 584--606.

Abstract:
This paper establishes the argmin of a random objective function to be unique almost surely. This paper first formulates a general result that proves almost sure uniqueness without convexity of the objective function. The general result is then applied to a variety of applications in statistics. Four applications are discussed, including uniqueness of M-estimators, both classical likelihood and penalized likelihood estimators, and two applications of the argmin theorem, threshold regression and weak identification.

Edgar Dobriban, William Leeb, Amit Singer.

Source: The Annals of Statistics, Volume 48, Number 1, 491--513.

Abstract:
We consider the linearly transformed spiked model , where the observations $Y_{i}$ are noisy linear transforms of unobserved signals of interest $X_{i}$: egin{equation*}Y_{i}=A_{i}X_{i}+varepsilon_{i},end{equation*} for $i=1,ldots ,n$. The transform matrices $A_{i}$ are also observed. We model the unobserved signals (or regression coefficients) $X_{i}$ as vectors lying on an unknown low-dimensional space. Given only $Y_{i}$ and $A_{i}$ how should we predict or recover their values? The naive approach of performing regression for each observation separately is inaccurate due to the large noise level. Instead, we develop optimal methods for predicting $X_{i}$ by “borrowing strength” across the different samples. Our linear empirical Bayes methods scale to large datasets and rely on weak moment assumptions. We show that this model has wide-ranging applications in signal processing, deconvolution, cryo-electron microscopy, and missing data with noise. For missing data, we show in simulations that our methods are more robust to noise and to unequal sampling than well-known matrix completion methods.

Michael Schweinberger, Jonathan Stewart.

Source: The Annals of Statistics, Volume 48, Number 1, 374--396.

Abstract:
Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple example of a random graph with additional structure is a random graph with neighborhoods and local dependence within neighborhoods. We develop the first concentration and consistency results for maximum likelihood and $M$-estimators of a wide range of canonical and curved exponential-family models of random graphs with local dependence. All results are nonasymptotic and applicable to random graphs with finite populations of nodes, although asymptotic consistency results can be obtained as well. In addition, we show that additional structure can facilitate subgraph-to-graph estimation, and present concentration results for subgraph-to-graph estimators. As an application, we consider popular curved exponential-family models of random graphs, with local dependence induced by transitivity and parameter vectors whose dimensions depend on the number of nodes.

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.

Dimitris Bertsimas, Bart Van Parys.

Source: The Annals of Statistics, Volume 48, Number 1, 300--323.

Abstract:
We present a novel binary convex reformulation of the sparse regression problem that constitutes a new duality perspective. We devise a new cutting plane method and provide evidence that it can solve to provable optimality the sparse regression problem for sample sizes $n$ and number of regressors $p$ in the 100,000s, that is, two orders of magnitude better than the current state of the art, in seconds. The ability to solve the problem for very high dimensions allows us to observe new phase transition phenomena. Contrary to traditional complexity theory which suggests that the difficulty of a problem increases with problem size, the sparse regression problem has the property that as the number of samples $n$ increases the problem becomes easier in that the solution recovers 100% of the true signal, and our approach solves the problem extremely fast (in fact faster than Lasso), while for small number of samples $n$, our approach takes a larger amount of time to solve the problem, but importantly the optimal solution provides a statistically more relevant regressor. We argue that our exact sparse regression approach presents a superior alternative over heuristic methods available at present.

Stephen M. S. Lee, Puyudi Yang.

Source: The Annals of Statistics, Volume 48, Number 1, 274--299.

Abstract:
Suppose that a confidence region is desired for a subvector $ heta $ of a multidimensional parameter $xi =( heta ,psi )$, based on an M-estimator $hat{xi }_{n}=(hat{ heta }_{n},hat{psi }_{n})$ calculated from a random sample of size $n$. Under nonstandard conditions $hat{xi }_{n}$ often converges at a nonregular rate $r_{n}$, in which case consistent estimation of the distribution of $r_{n}(hat{ heta }_{n}- heta )$, a pivot commonly chosen for confidence region construction, is most conveniently effected by the $m$ out of $n$ bootstrap. The above choice of pivot has three drawbacks: (i) the shape of the region is either subjectively prescribed or controlled by a computationally intensive depth function; (ii) the region is not transformation equivariant; (iii) $hat{xi }_{n}$ may not be uniquely defined. To resolve the above difficulties, we propose a one-dimensional pivot derived from the criterion function, and prove that its distribution can be consistently estimated by the $m$ out of $n$ bootstrap, or by a modified version of the perturbation bootstrap. This leads to a new method for constructing confidence regions which are transformation equivariant and have shapes driven solely by the criterion function. A subsampling procedure is proposed for selecting $m$ in practice. Empirical performance of the new method is illustrated with examples drawn from different nonstandard M-estimation settings. Extension of our theory to row-wise independent triangular arrays is also explored.

Xi Chen, Jason D. Lee, Xin T. Tong, Yichen Zhang.

Source: The Annals of Statistics, Volume 48, Number 1, 251--273.

Abstract:
The stochastic gradient descent (SGD) algorithm has been widely used in statistical estimation for large-scale data due to its computational and memory efficiency. While most existing works focus on the convergence of the objective function or the error of the obtained solution, we investigate the problem of statistical inference of true model parameters based on SGD when the population loss function is strongly convex and satisfies certain smoothness conditions. Our main contributions are twofold. First, in the fixed dimension setup, we propose two consistent estimators of the asymptotic covariance of the average iterate from SGD: (1) a plug-in estimator, and (2) a batch-means estimator, which is computationally more efficient and only uses the iterates from SGD. Both proposed estimators allow us to construct asymptotically exact confidence intervals and hypothesis tests. Second, for high-dimensional linear regression, using a variant of the SGD algorithm, we construct a debiased estimator of each regression coefficient that is asymptotically normal. This gives a one-pass algorithm for computing both the sparse regression coefficients and confidence intervals, which is computationally attractive and applicable to online data.

Adityanand Guntuboyina, Donovan Lieu, Sabyasachi Chatterjee, Bodhisattva Sen.

Source: The Annals of Statistics, Volume 48, Number 1, 205--229.

Abstract:
We study trend filtering, a relatively recent method for univariate nonparametric regression. For a given integer $rgeq1$, the $r$th order trend filtering estimator is defined as the minimizer of the sum of squared errors when we constrain (or penalize) the sum of the absolute $r$th order discrete derivatives of the fitted function at the design points. For $r=1$, the estimator reduces to total variation regularization which has received much attention in the statistics and image processing literature. In this paper, we study the performance of the trend filtering estimator for every $rgeq1$, both in the constrained and penalized forms. Our main results show that in the strong sparsity setting when the underlying function is a (discrete) spline with few “knots,” the risk (under the global squared error loss) of the trend filtering estimator (with an appropriate choice of the tuning parameter) achieves the parametric $n^{-1}$-rate, up to a logarithmic (multiplicative) factor. Our results therefore provide support for the use of trend filtering, for every $rgeq1$, in the strong sparsity setting.

Guangyu Zhu, Zhihua Su.

Source: The Annals of Statistics, Volume 48, Number 1, 161--182.

Abstract:
Sparse partial least squares (SPLS) is widely used in applied sciences as a method that performs dimension reduction and variable selection simultaneously in linear regression. Several implementations of SPLS have been derived, among which the SPLS proposed in Chun and Keleş ( J. R. Stat. Soc. Ser. B. Stat. Methodol. 72 (2010) 3–25) is very popular and highly cited. However, for all of these implementations, the theoretical properties of SPLS are largely unknown. In this paper, we propose a new version of SPLS, called the envelope-based SPLS, using a connection between envelope models and partial least squares (PLS). We establish the consistency, oracle property and asymptotic normality of the envelope-based SPLS estimator. The large-sample scenario and high-dimensional scenario are both considered. We also develop the envelope-based SPLS estimators under the context of generalized linear models, and discuss its theoretical properties including consistency, oracle property and asymptotic distribution. Numerical experiments and examples show that the envelope-based SPLS estimator has better variable selection and prediction performance over the SPLS estimator ( J. R. Stat. Soc. Ser. B. Stat. Methodol. 72 (2010) 3–25).

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.

Florentina Bunea, Christophe Giraud, Xi Luo, Martin Royer, Nicolas Verzelen.

Source: The Annals of Statistics, Volume 48, Number 1, 111--137.

Abstract:
The problem of variable clustering is that of estimating groups of similar components of a $p$-dimensional vector $X=(X_{1},ldots ,X_{p})$ from $n$ independent copies of $X$. There exists a large number of algorithms that return data-dependent groups of variables, but their interpretation is limited to the algorithm that produced them. An alternative is model-based clustering, in which one begins by defining population level clusters relative to a model that embeds notions of similarity. Algorithms tailored to such models yield estimated clusters with a clear statistical interpretation. We take this view here and introduce the class of $G$-block covariance models as a background model for variable clustering. In such models, two variables in a cluster are deemed similar if they have similar associations will all other variables. This can arise, for instance, when groups of variables are noise corrupted versions of the same latent factor. We quantify the difficulty of clustering data generated from a $G$-block covariance model in terms of cluster proximity, measured with respect to two related, but different, cluster separation metrics. We derive minimax cluster separation thresholds, which are the metric values below which no algorithm can recover the model-defined clusters exactly, and show that they are different for the two metrics. We therefore develop two algorithms, COD and PECOK, tailored to $G$-block covariance models, and study their minimax-optimality with respect to each metric. Of independent interest is the fact that the analysis of the PECOK algorithm, which is based on a corrected convex relaxation of the popular $K$-means algorithm, provides the first statistical analysis of such algorithms for variable clustering. Additionally, we compare our methods with another popular clustering method, spectral clustering. Extensive simulation studies, as well as our data analyses, confirm the applicability of our approach.

John Goes, Gilad Lerman, Boaz Nadler.

Source: The Annals of Statistics, Volume 48, Number 1, 86--110.

Abstract:
Estimating a high-dimensional sparse covariance matrix from a limited number of samples is a fundamental task in contemporary data analysis. Most proposals to date, however, are not robust to outliers or heavy tails. Toward bridging this gap, in this work we consider estimating a sparse shape matrix from $n$ samples following a possibly heavy-tailed elliptical distribution. We propose estimators based on thresholding either Tyler’s M-estimator or its regularized variant. We prove that in the joint limit as the dimension $p$ and the sample size $n$ tend to infinity with $p/n ogamma>0$, our estimators are minimax rate optimal. Results on simulated data support our theoretical analysis.

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.

Emmanuel J. Candès, Pragya Sur.

Source: The Annals of Statistics, Volume 48, Number 1, 27--42.

Abstract:
This paper rigorously establishes that the existence of the maximum likelihood estimate (MLE) in high-dimensional logistic regression models with Gaussian covariates undergoes a sharp “phase transition.” We introduce an explicit boundary curve $h_{mathrm{MLE}}$, parameterized by two scalars measuring the overall magnitude of the unknown sequence of regression coefficients, with the following property: in the limit of large sample sizes $n$ and number of features $p$ proportioned in such a way that $p/n ightarrow kappa $, we show that if the problem is sufficiently high dimensional in the sense that $kappa >h_{mathrm{MLE}}$, then the MLE does not exist with probability one. Conversely, if $kappa <h_{mathrm{MLE}}$, the MLE asymptotically exists with probability one.

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.

Holger Dette, Weichi Wu.

Source: The Annals of Statistics, Volume 47, Number 6, 3578--3608.

Abstract:
This paper considers the problem of testing if a sequence of means $(mu_{t})_{t=1,ldots ,n}$ of a nonstationary time series $(X_{t})_{t=1,ldots ,n}$ is stable in the sense that the difference of the means $mu_{1}$ and $mu_{t}$ between the initial time $t=1$ and any other time is smaller than a given threshold, that is $|mu_{1}-mu_{t}|leq c$ for all $t=1,ldots ,n$. A test for hypotheses of this type is developed using a bias corrected monotone rearranged local linear estimator and asymptotic normality of the corresponding test statistic is established. As the asymptotic variance depends on the location of the roots of the equation $|mu_{1}-mu_{t}|=c$ a new bootstrap procedure is proposed to obtain critical values and its consistency is established. As a consequence we are able to quantitatively describe relevant deviations of a nonstationary sequence from its initial value. The results are illustrated by means of a simulation study and by analyzing data examples.