Annals of Statistics最新文献_第10页

LINEAR HYPOTHESIS TESTING FOR HIGH DIMENSIONAL GENERALIZED LINEAR MODELS. 高维广义线性模型的线性假设检验。

IF 3.2 1区数学

Annals of Statistics Pub Date : 2019-10-01 Epub Date: 2019-08-03 DOI: 10.1214/18-AOS1761

Chengchun Shi, Rui Song, Zhao Chen, Runze Li

引用次数: 0

ON TESTING CONDITIONAL QUALITATIVE TREATMENT EFFECTS. 关于测试有条件的定性治疗效果。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2019-08-01 Epub Date: 2019-05-21 DOI: 10.1214/18-AOS1750

Chengchun Shi, Rui Song, Wenbin Lu

{"title":"ON TESTING CONDITIONAL QUALITATIVE TREATMENT EFFECTS.","authors":"Chengchun Shi, Rui Song, Wenbin Lu","doi":"10.1214/18-AOS1750","DOIUrl":"10.1214/18-AOS1750","url":null,"abstract":"Precision medicine is an emerging medical paradigm that focuses on finding the most effective treatment strategy tailored for individual patients. In the literature, most of the existing works focused on estimating the optimal treatment regime. However, there has been less attention devoted to hypothesis testing regarding the optimal treatment regime. In this paper, we first introduce the notion of conditional qualitative treatment effects (CQTE) of a set of variables given another set of variables and provide a class of equivalent representations for the null hypothesis of no CQTE. The proposed definition of CQTE does not assume any parametric form for the optimal treatment rule and plays an important role for assessing the incremental value of a set of new variables in optimal treatment decision making conditional on an existing set of prescriptive variables. We then propose novel testing procedures for no CQTE based on kernel estimation of the conditional contrast functions. We show that our test statistics have asymptotically correct size and non-negligible power against some nonstandard local alternatives. The empirical performance of the proposed tests are evaluated by simulations and an application to an AIDS data set.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"47 4","pages":"2348-2377"},"PeriodicalIF":4.5,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/18-AOS1750","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37047929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

A ROBUST AND EFFICIENT APPROACH TO CAUSAL INFERENCE BASED ON SPARSE SUFFICIENT DIMENSION REDUCTION. 一种基于稀疏充分降维的稳健有效的因果推理方法。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2019-06-01 Epub Date: 2019-02-13 DOI: 10.1214/18-AOS1722

Shujie Ma, Liping Zhu, Zhiwei Zhang, Chih-Ling Tsai, Raymond J Carroll

{"title":"A ROBUST AND EFFICIENT APPROACH TO CAUSAL INFERENCE BASED ON SPARSE SUFFICIENT DIMENSION REDUCTION.","authors":"Shujie Ma, Liping Zhu, Zhiwei Zhang, Chih-Ling Tsai, Raymond J Carroll","doi":"10.1214/18-AOS1722","DOIUrl":"10.1214/18-AOS1722","url":null,"abstract":"A fundamental assumption used in causal inference with observational data is that treatment assignment is ignorable given measured confounding variables. This assumption of no missing confounders is plausible if a large number of baseline covariates are included in the analysis, as we often have no prior knowledge of which variables can be important confounders. Thus, estimation of treatment effects with a large number of covariates has received considerable attention in recent years. Most existing methods require specifying certain parametric models involving the outcome, treatment and confounding variables, and employ a variable selection procedure to identify confounders. However, selection of a proper set of confounders depends on correct specification of the working models. The bias due to model misspecification and incorrect selection of confounding variables can yield misleading results. We propose a robust and efficient approach for inference about the average treatment effect via a flexible modeling strategy incorporating penalized variable selection. Specifically, we consider an estimator constructed based on an efficient influence function that involves a propensity score and an outcome regression. We then propose a new sparse sufficient dimension reduction method to estimate these two functions without making restrictive parametric modeling assumptions. The proposed estimator of the average treatment effect is asymptotically normal and semiparametrically efficient without the need for variable selection consistency. The proposed methods are illustrated via simulation studies and a biomedical application.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"47 3","pages":"1505-1535"},"PeriodicalIF":4.5,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/18-AOS1722","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37359979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 25

FEATURE ELIMINATION IN KERNEL MACHINES IN MODERATELY HIGH DIMENSIONS. 中等高维内核机中的特征消除。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2019-02-01 DOI: 10.1214/18-AOS1696

Sayan Dasgupta, Yair Goldberg, Michael R Kosorok

引用次数: 18

NONPARAMETRIC TESTING FOR MULTIPLE SURVIVAL FUNCTIONS WITH NON-INFERIORITY MARGINS. 具有非劣效边际的多个生存函数的非参数检验。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2019-02-01 Epub Date: 2018-11-30 DOI: 10.1214/18-AOS1686

Hsin-Wen Chang, Ian W McKeague

引用次数: 5

SPECTRAL METHOD AND REGULARIZED MLE ARE BOTH OPTIMAL FOR TOP-K RANKING. 谱方法和正则化MLE都是TOP-K排序的最优方法。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2019-01-01 Epub Date: 2019-05-21 DOI: 10.1214/18-AOS1745

Yuxin Chen, Jianqing Fan, Cong Ma, Kaizheng Wang

{"title":"SPECTRAL METHOD AND REGULARIZED MLE ARE BOTH OPTIMAL FOR TOP-K RANKING.","authors":"Yuxin Chen, Jianqing Fan, Cong Ma, Kaizheng Wang","doi":"10.1214/18-AOS1745","DOIUrl":"https://doi.org/10.1214/18-AOS1745","url":null,"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 towards 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 non-iterative procedures. Along the way, we derive an elementary eigenvector perturbation bound for probability transition matrices, which parallels the Davis-Kahan <math><mtext>Θ</mtext></math> theorem for symmetric matrices. This also allows us to close the gap between the <math><msub><mi>l</mi> <mn>2</mn></msub> </math> error upper bound for the spectral method and the minimax lower limit.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"47 4","pages":"2204-2235"},"PeriodicalIF":4.5,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/18-AOS1745","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41189337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 102

HYPOTHESIS TESTING ON LINEAR STRUCTURES OF HIGH DIMENSIONAL COVARIANCE MATRIX. 高维协方差矩阵线性结构的假设检验。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2019-01-01 Epub Date: 2019-10-31 DOI: 10.1214/18-AOS1779

Shurong Zheng, Zhao Chen, Hengjian Cui, Runze Li

{"title":"HYPOTHESIS TESTING ON LINEAR STRUCTURES OF HIGH DIMENSIONAL COVARIANCE MATRIX.","authors":"Shurong Zheng, Zhao Chen, Hengjian Cui, Runze Li","doi":"10.1214/18-AOS1779","DOIUrl":"https://doi.org/10.1214/18-AOS1779","url":null,"abstract":"This paper is concerned with test of significance on high dimensional covariance structures, and aims to develop a unified framework for testing commonly-used linear covariance structures. We first construct a consistent estimator for parameters involved in the linear covariance structure, and then develop two tests for the linear covariance structures based on entropy loss and quadratic loss used for covariance matrix estimation. To study the asymptotic properties of the proposed tests, we study related high dimensional random matrix theory, and establish several highly useful asymptotic results. With the aid of these asymptotic results, we derive the limiting distributions of these two tests under the null and alternative hypotheses. We further show that the quadratic loss based test is asymptotically unbiased. We conduct Monte Carlo simulation study to examine the finite sample performance of the two tests. Our simulation results show that the limiting null distributions approximate their null distributions quite well, and the corresponding asymptotic critical values keep Type I error rate very well. Our numerical comparison implies that the proposed tests outperform existing ones in terms of controlling Type I error rate and power. Our simulation indicates that the test based on quadratic loss seems to have better power than the test based on entropy loss.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"47 6","pages":"3300-3334"},"PeriodicalIF":4.5,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6910252/pdf/nihms-1022732.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37459228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 18

UNIFORMLY VALID POST-REGULARIZATION CONFIDENCE REGIONS FOR MANY FUNCTIONAL PARAMETERS IN Z-ESTIMATION FRAMEWORK. Z估计框架中许多函数参数的一致有效正则化后置信域。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2018-12-01 Epub Date: 2018-09-11 DOI: 10.1214/17-AOS1671

Alexandre Belloni, Victor Chernozhukov, Denis Chetverikov, Ying Wei

{"title":"UNIFORMLY VALID POST-REGULARIZATION CONFIDENCE REGIONS FOR MANY FUNCTIONAL PARAMETERS IN Z-ESTIMATION FRAMEWORK.","authors":"Alexandre Belloni, Victor Chernozhukov, Denis Chetverikov, Ying Wei","doi":"10.1214/17-AOS1671","DOIUrl":"10.1214/17-AOS1671","url":null,"abstract":"In this paper, we develop procedures to construct simultaneous confidence bands for <math><mover><mi>p</mi> <mo>˜</mo></mover> </math> potentially infinite-dimensional parameters after model selection for general moment condition models where <math> <mrow><mover><mi>p</mi> <mo>˜</mo></mover> </mrow> </math> is potentially much larger than the sample size of available data, n. This allows us to cover settings with functional response data where each of the <math> <mrow><mover><mi>p</mi> <mo>˜</mo></mover> </mrow> </math> parameters is a function. The procedure is based on the construction of score functions that satisfy Neyman orthogonality condition approximately. The proposed simultaneous confidence bands rely on uniform central limit theorems for high-dimensional vectors (and not on Donsker arguments as we allow for <math> <mrow><mover><mi>p</mi> <mo>˜</mo></mover> <mo>≫</mo> <mi>n</mi></mrow> </math> ). To construct the bands, we employ a multiplier bootstrap procedure which is computationally efficient as it only involves resampling the estimated score functions (and does not require resolving the high-dimensional optimization problems). We formally apply the general theory to inference on regression coefficient process in the distribution regression model with a logistic link, where two implementations are analyzed in detail. Simulations and an application to real data are provided to help illustrate the applicability of the results.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"46 6B","pages":"3643-3675"},"PeriodicalIF":4.5,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/17-AOS1671","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37129329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 71

ASSESSING ROBUSTNESS OF CLASSIFICATION USING ANGULAR BREAKDOWN POINT. 使用角度分解点评估分类的稳健性。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2018-12-01 Epub Date: 2018-09-11 DOI: 10.1214/17-AOS1661

Junlong Zhao, Guan Yu, Yufeng Liu

引用次数: 7

A NEW PERSPECTIVE ON ROBUST M-ESTIMATION: FINITE SAMPLE THEORY AND APPLICATIONS TO DEPENDENCE-ADJUSTED MULTIPLE TESTING. 稳健M估计的新视角：有限样本理论及其在依赖调整多重检验中的应用。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2018-10-01 Epub Date: 2018-08-17 DOI: 10.1214/17-AOS1606

Wen-Xin Zhou, Koushiki Bose, Jianqing Fan, Han Liu

{"title":"A NEW PERSPECTIVE ON ROBUST M-ESTIMATION: FINITE SAMPLE THEORY AND APPLICATIONS TO DEPENDENCE-ADJUSTED MULTIPLE TESTING.","authors":"Wen-Xin Zhou, Koushiki Bose, Jianqing Fan, Han Liu","doi":"10.1214/17-AOS1606","DOIUrl":"10.1214/17-AOS1606","url":null,"abstract":"Heavy-tailed errors impair the accuracy of the least squares estimate, which can be spoiled by a single grossly outlying observation. As argued in the seminal work of Peter Huber in 1973 [Ann. Statist.1 (1973) 799-821], robust alternatives to the method of least squares are sorely needed. To achieve robustness against heavy-tailed sampling distributions, we revisit the Huber estimator from a new perspective by letting the tuning parameter involved diverge with the sample size. In this paper, we develop nonasymptotic concentration results for such an adaptive Huber estimator, namely, the Huber estimator with the tuning parameter adapted to sample size, dimension, and the variance of the noise. Specifically, we obtain a sub-Gaussian-type deviation inequality and a nonasymptotic Bahadur representation when noise variables only have finite second moments. The nonasymptotic results further yield two conventional normal approximation results that are of independent interest, the Berry-Esseen inequality and Cramér-type moderate deviation. As an important application to large-scale simultaneous inference, we apply these robust normal approximation results to analyze a dependence-adjusted multiple testing procedure for moderately heavy-tailed data. It is shown that the robust dependence-adjusted procedure asymptotically controls the overall false discovery proportion at the nominal level under mild moment conditions. Thorough numerical results on both simulated and real datasets are also provided to back up our theory.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"46 5","pages":"1904-1931"},"PeriodicalIF":4.5,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6133288/pdf/nihms926033.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36491731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0