Annals of Statistics最新文献

{"title":"The multi-armed bandit problem: An efficient nonparametric solution","authors":"H. Chan","doi":"10.1214/19-aos1809","DOIUrl":"https://doi.org/10.1214/19-aos1809","url":null,"abstract":"","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"48 1","pages":"346-373"},"PeriodicalIF":4.5,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48748922","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}

{"title":"Penalized generalized empirical likelihood with a diverging number of general estimating equations for censored data","authors":"Nian-Sheng Tang, Xiaodong Yan, Xingqiu Zhao","doi":"10.1214/19-aos1870","DOIUrl":"https://doi.org/10.1214/19-aos1870","url":null,"abstract":"This article considers simultaneous variable selection and parameter estimation as well as hypothesis testing in censored regression models with unspecified parametric likelihood. For the problem, we utilize certain growing dimensional general estimating equations and propose a penalized generalized empirical likelihood using the folded concave penalties. We first construct general estimating equations attaining the semiparametric efficiency bound with censored regression data and then establish the consistency and oracle properties of the penalized generalized empirical likelihood estimators. Furthermore, we show that the penalized generalized empirical likelihood ratio test statistic has an asymptotic standard central chi-squared distribution. The conditions of local and restricted global optimality of weighted penalized generalized empirical likelihood estimators are also discussed. We present an two-layer iterative algorithm for efficient implementation, and rigorously investigate its convergence property. The good performance of the proposed methods are demonstrated by extensive simulation studies and a real data example is provided for illustration.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"48 1","pages":"607-627"},"PeriodicalIF":4.5,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44061735","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}

{"title":"Sparse SIR: Optimal rates and adaptive estimation","authors":"Kai Tan, Lei Shi, Zhou Yu","doi":"10.1214/18-aos1791","DOIUrl":"https://doi.org/10.1214/18-aos1791","url":null,"abstract":"Sliced inverse regression (SIR) is an innovative and effective method for sufficient dimension reduction and data visualization. Recently, an impressive range of penalized SIR methods has been proposed to estimate the central subspace in a sparse fashion. Nonetheless, few of them considered the sparse sufficient dimension reduction from a decision-theoretic point of view. To address this issue, we in this paper establish the minimax rates of convergence for estimating the sparse SIR directions under various commonly used loss functions in the literature of sufficient dimension reduction. We also discover the possible trade-off between statistical guarantee and computational performance for sparse SIR. We finally propose an adaptive estimation scheme for sparse SIR which is computationally tractable and rate optimal. Numerical studies are carried out to confirm the theoretical properties of our proposed methods.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"48 1","pages":"64-85"},"PeriodicalIF":4.5,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43689262","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}

{"title":"CONSISTENT SELECTION OF THE NUMBER OF CHANGE-POINTS VIA SAMPLE-SPLITTING.","authors":"Changliang Zou,&nbsp;Guanghui Wang,&nbsp;Runze Li","doi":"10.1214/19-aos1814","DOIUrl":"https://doi.org/10.1214/19-aos1814","url":null,"abstract":"<p><p>In multiple change-point analysis, one of the major challenges is to estimate the number of change-points. Most existing approaches attempt to minimize a Schwarz information criterion which balances a term quantifying model fit with a penalization term accounting for model complexity that increases with the number of change-points and limits overfitting. However, different penalization terms are required to adapt to different contexts of multiple change-point problems and the optimal penalization magnitude usually varies from the model and error distribution. We propose a data-driven selection criterion that is applicable to most kinds of popular change-point detection methods, including binary segmentation and optimal partitioning algorithms. The key idea is to select the number of change-points that minimizes the squared prediction error, which measures the fit of a specified model for a new sample. We develop a cross-validation estimation scheme based on an order-preserved sample-splitting strategy, and establish its asymptotic selection consistency under some mild conditions. Effectiveness of the proposed selection criterion is demonstrated on a variety of numerical experiments and real-data examples.</p>","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"48 1","pages":"413-439"},"PeriodicalIF":4.5,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7397423/pdf/nihms-1022718.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38232848","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}

{"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}

{"title":"MODEL ASSISTED VARIABLE CLUSTERING: MINIMAX-OPTIMAL RECOVERY AND ALGORITHMS.","authors":"Florentina Bunea,&nbsp;Christophe Giraud,&nbsp;Xi Luo,&nbsp;Martin Royer,&nbsp;Nicolas Verzelen","doi":"10.1214/18-aos1794","DOIUrl":"https://doi.org/10.1214/18-aos1794","url":null,"abstract":"<p><p>The problem of variable clustering is that of estimating groups of similar components of a <i>p</i>-dimensional vector <i>X</i> = (<i>X</i> ₁, … , <i>X</i> _<i>p</i> ) from <i>n</i> independent copies of <i>X</i>. 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 <i>G</i>-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 <i>G</i>-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 <i>G</i>-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 <i>K</i>-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.</p>","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":" ","pages":"111-137"},"PeriodicalIF":4.5,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9286061/pdf/nihms-1765231.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40532443","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}

{"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}

{"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}

{"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}

{"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}