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Envelope-based sparse partial least squares 基于包络的稀疏偏最小二乘法
IF 4.5 1区 数学
Annals of Statistics Pub Date : 2020-02-01 DOI: 10.1214/18-aos1796
G. Zhu, Zhihua Su
{"title":"Envelope-based sparse partial least squares","authors":"G. Zhu, Zhihua Su","doi":"10.1214/18-aos1796","DOIUrl":"https://doi.org/10.1214/18-aos1796","url":null,"abstract":"","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"48 1","pages":"161-182"},"PeriodicalIF":4.5,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42464903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 23
Detecting relevant changes in the mean of nonstationary processes—A mass excess approach 检测非平稳过程均值的相关变化——一种质量过剩方法
IF 4.5 1区 数学
Annals of Statistics Pub Date : 2019-12-01 DOI: 10.1214/19-aos1811
H. Dette, Weichi Wu
{"title":"Detecting relevant changes in the mean of nonstationary processes—A mass excess approach","authors":"H. Dette, Weichi Wu","doi":"10.1214/19-aos1811","DOIUrl":"https://doi.org/10.1214/19-aos1811","url":null,"abstract":"This paper considers the problem of testing if a sequence of means (μt)t=1,...,n of a non-stationary time series (Xt)t=1,...,n is stable in the sense that the difference of the means μ1 and μt between the initial time t = 1 and any other time is smaller than a given threshold, that is |μ1 − μt| ≤ c for all t = 1, . . . , 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 |μ1 − μt| = 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 non-stationary sequence from its initial value. The results are illustrated by means of a simulation study and by analyzing data examples.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"47 1","pages":"3578-3608"},"PeriodicalIF":4.5,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43286673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 25
Joint convergence of sample autocovariance matrices when $p/nto 0$ with application $p/n为0$时样本自协方差矩阵的联合收敛性及其应用
IF 4.5 1区 数学
Annals of Statistics Pub Date : 2019-12-01 DOI: 10.1214/18-aos1785
M. Bhattacharjee, A. Bose
{"title":"Joint convergence of sample autocovariance matrices when $p/nto 0$ with application","authors":"M. Bhattacharjee, A. Bose","doi":"10.1214/18-aos1785","DOIUrl":"https://doi.org/10.1214/18-aos1785","url":null,"abstract":"Consider a high dimensional linear time series model where the dimension p and the sample size n grow in such a way that p/n → 0. Let Γ̂u be the uth order sample autocovariance matrix. We first show that the LSD of any symmetric polynomial in {Γ̂u, Γ̂u, u ≥ 0} exists under independence and moment assumptions on the driving sequence together with weak assumptions on the coefficient matrices. This LSD result, with some additional effort, implies the asymptotic normality of the trace of any polynomial in {Γ̂u, Γ̂u, u ≥ 0}. We also study similar results for several independent MA processes. We show applications of the above results to statistical inference problems such as in estimation of the unknown order of a highdimensional MA process and in graphical and significance tests for hypotheses on coefficient matrices of one or several such independent processes.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"47 1","pages":"3470-3503"},"PeriodicalIF":4.5,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46814252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
TEST FOR HIGH DIMENSIONAL CORRELATION MATRICES. 高维相关矩阵的测试。
IF 4.5 1区 数学
Annals of Statistics Pub Date : 2019-10-01 Epub Date: 2019-08-03 DOI: 10.1214/18-AOS1768
Shurong Zheng, Guanghui Cheng, Jianhua Guo, Hongtu Zhu
{"title":"TEST FOR HIGH DIMENSIONAL CORRELATION MATRICES.","authors":"Shurong Zheng,&nbsp;Guanghui Cheng,&nbsp;Jianhua Guo,&nbsp;Hongtu Zhu","doi":"10.1214/18-AOS1768","DOIUrl":"https://doi.org/10.1214/18-AOS1768","url":null,"abstract":"<p><p>Testing correlation structures has attracted extensive attention in the literature due to both its importance in real applications and several major theoretical challenges. The aim of this paper is to develop a general framework of testing correlation structures for the one-, two-, and multiple sample testing problems under a high-dimensional setting when both the sample size and data dimension go to infinity. Our test statistics are designed to deal with both the dense and sparse alternatives. We systematically investigate the asymptotic null distribution, power function, and unbiasedness of each test statistic. Theoretically, we make great efforts to deal with the non-independency of all random matrices of the sample correlation matrices. We use simulation studies and real data analysis to illustrate the versatility and practicability of our test statistics.</p>","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"47 5","pages":"2887-2921"},"PeriodicalIF":4.5,"publicationDate":"2019-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/18-AOS1768","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41189339","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
EIGENVALUE DISTRIBUTIONS OF VARIANCE COMPONENTS ESTIMATORS IN HIGH-DIMENSIONAL RANDOM EFFECTS MODELS. 高维随机效应模型中方差分量估计量的特征值分布。
IF 4.5 1区 数学
Annals of Statistics Pub Date : 2019-10-01 Epub Date: 2019-08-03 DOI: 10.1214/18-AOS1767
Fan Zhou, Iain M Johnstone
{"title":"EIGENVALUE DISTRIBUTIONS OF VARIANCE COMPONENTS ESTIMATORS IN HIGH-DIMENSIONAL RANDOM EFFECTS MODELS.","authors":"Fan Zhou,&nbsp;Iain M Johnstone","doi":"10.1214/18-AOS1767","DOIUrl":"https://doi.org/10.1214/18-AOS1767","url":null,"abstract":"<p><p>We study the spectra of MANOVA estimators for variance component covariance matrices in multivariate random effects models. When the dimensionality of the observations is large and comparable to the number of realizations of each random effect, we show that the empirical spectra of such estimators are well-approximated by deterministic laws. The Stieltjes transforms of these laws are characterized by systems of fixed-point equations, which are numerically solvable by a simple iterative procedure. Our proof uses operator-valued free probability theory, and we establish a general asymptotic freeness result for families of rectangular orthogonally-invariant random matrices, which is of independent interest. Our work is motivated in part by the estimation of components of covariance between multiple phenotypic traits in quantitative genetics, and we specialize our results to common experimental designs that arise in this application.</p>","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"47 5","pages":"2855-2886"},"PeriodicalIF":4.5,"publicationDate":"2019-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/18-AOS1767","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41189338","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: 13
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
{"title":"LINEAR HYPOTHESIS TESTING FOR HIGH DIMENSIONAL GENERALIZED LINEAR MODELS.","authors":"Chengchun Shi, Rui Song, Zhao Chen, Runze Li","doi":"10.1214/18-AOS1761","DOIUrl":"10.1214/18-AOS1761","url":null,"abstract":"<p><p>This paper is concerned with testing linear hypotheses in high-dimensional generalized linear models. To deal with linear hypotheses, we first propose constrained partial regularization method and study its statistical properties. We further introduce an algorithm for solving regularization problems with folded-concave penalty functions and linear constraints. To test linear hypotheses, we propose a partial penalized likelihood ratio test, a partial penalized score test and a partial penalized Wald test. We show that the limiting null distributions of these three test statistics are χ<sup>2</sup> distribution with the same degrees of freedom, and under local alternatives, they asymptotically follow non-central χ<sup>2</sup> distributions with the same degrees of freedom and noncentral parameter, provided the number of parameters involved in the test hypothesis grows to ∞ at a certain rate. Simulation studies are conducted to examine the finite sample performance of the proposed tests. Empirical analysis of a real data example is used to illustrate the proposed testing procedures.</p>","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"47 5 1","pages":"2671-2703"},"PeriodicalIF":3.2,"publicationDate":"2019-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6750760/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48392668","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
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,&nbsp;Rui Song,&nbsp;Wenbin Lu","doi":"10.1214/18-AOS1750","DOIUrl":"10.1214/18-AOS1750","url":null,"abstract":"<p><p>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.</p>","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,&nbsp;Liping Zhu,&nbsp;Zhiwei Zhang,&nbsp;Chih-Ling Tsai,&nbsp;Raymond J Carroll","doi":"10.1214/18-AOS1722","DOIUrl":"10.1214/18-AOS1722","url":null,"abstract":"<p><p>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.</p>","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
{"title":"FEATURE ELIMINATION IN KERNEL MACHINES IN MODERATELY HIGH DIMENSIONS.","authors":"Sayan Dasgupta,&nbsp;Yair Goldberg,&nbsp;Michael R Kosorok","doi":"10.1214/18-AOS1696","DOIUrl":"https://doi.org/10.1214/18-AOS1696","url":null,"abstract":"<p><p>We develop an approach for feature elimination in statistical learning with kernel machines, based on recursive elimination of features. We present theoretical properties of this method and show that it is uniformly consistent in finding the correct feature space under certain generalized assumptions. We present a few case studies to show that the assumptions are met in most practical situations and present simulation results to demonstrate performance of the proposed approach.</p>","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"47 1","pages":"497-526"},"PeriodicalIF":4.5,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/18-AOS1696","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36792835","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
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
{"title":"NONPARAMETRIC TESTING FOR MULTIPLE SURVIVAL FUNCTIONS WITH NON-INFERIORITY MARGINS.","authors":"Hsin-Wen Chang,&nbsp;Ian W McKeague","doi":"10.1214/18-AOS1686","DOIUrl":"10.1214/18-AOS1686","url":null,"abstract":"<p><p>New nonparametric tests for the ordering of multiple survival functions are developed with the possibility of right censorship taken into account. The motivation comes from non-inferiority trials with multiple treatments. The proposed tests are based on nonparametric likelihood ratio statistics, which are known to provide more powerful tests than Wald-type procedures, but in this setting have only been studied for pairs of survival functions or in the absence of censoring. We introduce a novel type of pool adjacent violator algorithm that leads to a complete solution of the problem. The limit distributions can be expressed as weighted sums of squares involving projections of certain Gaussian processes onto the given ordered alternative. A simulation study shows that the new procedures have superior power to a competing combined-pairwise Cox model approach. We illustrate the proposed methods using data from a three-arm non-inferiority trial.</p>","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"47 1","pages":"205-232"},"PeriodicalIF":4.5,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/18-AOS1686","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37341004","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: 5
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