Annals of Statistics最新文献_第10页

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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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

ANALYSIS OF "LEARN-AS-YOU-GO" (LAGO) STUDIES. “随学随走”(lago)研究分析。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2018-08-20 DOI: 10.1214/20-AOS1978

D. Nevo, J. Lok, D. Spiegelman

引用次数: 4

LARGE COVARIANCE ESTIMATION THROUGH ELLIPTICAL FACTOR MODELS. 通过椭圆因子模型的大协方差估计。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2018-08-01 Epub Date: 2018-06-27 DOI: 10.1214/17-AOS1588

Jianqing Fan, Han Liu, Weichen Wang

引用次数: 84

Consistency and convergence rate of phylogenetic inference via regularization. 基于正则化的系统发育推理的一致性和收敛率。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2018-08-01 Epub Date: 2018-06-27 DOI: 10.1214/17-AOS1592

Vu Dinh, Lam Si Tung Ho, Marc A Suchard, Frederick A Matsen

{"title":"Consistency and convergence rate of phylogenetic inference via regularization.","authors":"Vu Dinh, Lam Si Tung Ho, Marc A Suchard, Frederick A Matsen","doi":"10.1214/17-AOS1592","DOIUrl":"https://doi.org/10.1214/17-AOS1592","url":null,"abstract":"It is common in phylogenetics to have some, perhaps partial, information about the overall evolutionary tree of a group of organisms and wish to find an evolutionary tree of a specific gene for those organisms. There may not be enough information in the gene sequences alone to accurately reconstruct the correct \"gene tree.\" Although the gene tree may deviate from the \"species tree\" due to a variety of genetic processes, in the absence of evidence to the contrary it is parsimonious to assume that they agree. A common statistical approach in these situations is to develop a likelihood penalty to incorporate such additional information. Recent studies using simulation and empirical data suggest that a likelihood penalty quantifying concordance with a species tree can significantly improve the accuracy of gene tree reconstruction compared to using sequence data alone. However, the consistency of such an approach has not yet been established, nor have convergence rates been bounded. Because phylogenetics is a non-standard inference problem, the standard theory does not apply. In this paper, we propose a penalized maximum likelihood estimator for gene tree reconstruction, where the penalty is the square of the Billera-Holmes-Vogtmann geodesic distance from the gene tree to the species tree. We prove that this method is consistent, and derive its convergence rate for estimating the discrete gene tree structure and continuous edge lengths (representing the amount of evolution that has occurred on that branch) simultaneously. We find that the regularized estimator is \"adaptive fast converging,\" meaning that it can reconstruct all edges of length greater than any given threshold from gene sequences of polynomial length. Our method does not require the species tree to be known exactly; in fact, our asymptotic theory holds for any such guide tree.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/17-AOS1592","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36592809","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: 8