6期

最新文章

• QUANTILE REGRESSION UNDER MEMORY CONSTRAINT AI翻译
  作者：Chen, Xi; Liu, Weidong; Zhang, Yichen
  作者单位：New York University; Shanghai Jiao Tong University; Shanghai Jiao Tong University
  摘要：This paper studies the inference problem in quantile regression (QR) for a large sample size n but under a limited memory constraint, where the memory can only store a small batch of data of size m. A natural method is the naive divide-and-conquer approach, which splits data into batches of size m, computes the local QR estimator for each batch and then aggregates the estimators via averaging. However, this method only works when n = o(m(2)) and is computationally expensive. This paper propose...
• JOINT CONVERGENCE OF SAMPLE AUTOCOVARIANCE MATRICES WHEN p/n → 0 WITH APPLICATION AI翻译
  作者：Bhattacharjee, Monika; Bose, Arup
  作者单位：State University System of Florida; University of Florida; Indian Statistical Institute; Indian Statistical Institute Kolkata
  摘要：Consider a high-dimensional linear time series model where the dimen- sion p and the sample size n grow in such a way that p/n -> 0. Let (Gamma) over cap (u) be the uth order sample autocovariance matrix. We first show that the LSD of any symmetric polynomial in {(Gamma) over cap (u) , (Gamma) over cap (u)*, 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, i...
• A SMEARY CENTRAL LIMIT THEOREM FOR MANIFOLDS WITH APPLICATION TO HIGH-DIMENSIONAL SPHERES AI翻译
  作者：Eltzner, Benjamin; Huckemann, Stephan F.
  作者单位：University of Gottingen
  摘要：The (CLT) central limit theorems for generalized Frechet means (data descriptors assuming values in manifolds, such as intrinsic means, geodesics, etc.) on manifolds from the literature are only valid if a certain empirical process of Hessians of the Frechet function converges suitably, as in the proof of the prototypical BP-CLT [Ann. Statist. 33 (2005) 1225-1259]. This is not valid in many realistic scenarios and we provide for a new very general CLT. In particular, this includes scenarios wh...
• ACTIVE RANKING FROM PAIRWISE COMPARISONS AND WHEN PARAMETRIC ASSUMPTIONS DO NOT HELP AI翻译
  作者：Heckel, Reinhard; Shah, Nihar B.; Ramchandran, Kannan; Wainwright, Martin J.
  作者单位：Rice University; Carnegie Mellon University; Carnegie Mellon University; University of California System; University of California Berkeley; University of California System; University of California Berkeley
  摘要：We consider sequential or active ranking of a set of n items based on noisy pairwise comparisons. Items are ranked according to the probability that a given item beats a randomly chosen item, and ranking refers to partitioning the items into sets of prespecified sizes according to their scores. This notion of ranking includes as special cases the identification of the top-k items and the total ordering of the items. We first analyze a sequential ranking algorithm that counts the number of comp...
• MINIMAX POSTERIOR CONVERGENCE RATES AND MODEL SELECTION CONSISTENCY IN HIGH-DIMENSIONAL DAG MODELS BASED ON SPARSE CHOLESKY FACTORS AI翻译
  作者：Lee, Kyoungjae; Lee, Jaeyong; Lin, Lizhen
  作者单位：University of Notre Dame; University of Notre Dame; Seoul National University (SNU); Inha University
  摘要：In this paper we study the high-dimensional sparse directed acyclic graph (DAG) models under the empirical sparse Cholesky prior. Among our results, strong model selection consistency or graph selection consistency is obtained under more general conditions than those in the existing literature. Compared to Cao, Khare and Ghosh [Ann. Statist. (2019) 47 319-348], the required conditions are weakened in terms of the dimensionality, sparsity and lower bound of the nonzero elements in the Cholesky ...
• INTRINSIC RIEMANNIAN FUNCTIONAL DATA ANALYSIS AI翻译
  作者：Lin, Zhenhua; Yao, Fang
  作者单位：National University of Singapore; Peking University
  摘要：In this work we develop a novel and foundational framework for analyzing general Riemannian functional data, in particular a new development of tensor Hilbert spaces along curves on a manifold. Such spaces enable us to derive Karhunen-Loeve expansion for Riemannian random processes. This framework also features an approach to compare objects from different tensor Hilbert spaces, which paves the way for asymptotic analysis in Riemannian functional data analysis. Built upon intrinsic geometric c...
• HYPOTHESIS TESTING ON LINEAR STRUCTURES OF HIGH-DIMENSIONAL COVARIANCE MATRIX AI翻译
  作者：Zheng, Shurong; Chen, Zhao; Cui, Hengjian; Li, Runze
  作者单位：Northeast Normal University - China; Northeast Normal University - China; Capital Normal University; Fudan University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
  摘要：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 st...
• ON OPTIMAL DESIGNS FOR NONREGULAR MODELS AI翻译
  作者：Lin, Yi; Martin, Ryan; Yang, Min
  作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; North Carolina State University
  摘要：Classically, Fisher information is the relevant object in defining optimal experimental designs. However, for models that lack certain regularity, the Fisher information does not exist, and hence, there is no notion of design optimality available in the literature. This article seeks to fill the gap by proposing a so-called Hellinger information, which generalizes Fisher information in the sense that the two measures agree in regular problems, but the former also exists for certain types of no...
• STATISTICAL INFERENCE FOR AUTOREGRESSIVE MODELS UNDER HETEROSCEDASTICITY OF UNKNOWN FORM AI翻译
  作者：Zhu, Ke
  作者单位：University of Hong Kong
  摘要：This paper provides an entire inference procedure for the autoregressive model under (conditional) heteroscedasticity of unknown form with a finite variance. We first establish the asymptotic normality of the weighted least absolute deviations estimator (LADE) for the model. Second, we develop the random weighting (RW) method to estimate its asymptotic covariance matrix, leading to the implementation of the Wald test. Third, we construct a portmanteau test for model checking, and use the RW me...
• TRACY-WIDOM LIMIT FOR KENDALL'S TAU AI翻译
  作者：Bao, Zhigang
  作者单位：Hong Kong University of Science & Technology
  摘要：In this paper, we study a high-dimensional random matrix model from nonparametric statistics called the Kendall rank correlation matrix, which is a natural multivariate extension of the Kendall rank correlation coefficient. We establish the Tracy-Widom law for its largest eigenvalue. It is the first Tracy-Widom law for a nonparametric random matrix model, and also the first Tracy-Widom law for a high-dimensional U-statistic.