2019

最新文章

• 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...
• ESTIMATION OF LARGE COVARIANCE AND PRECISION MATRICES FROM TEMPORALLY DEPENDENT OBSERVATIONS AI翻译
  作者：Shu, Hai; Nan, Bin
  作者单位：University of Michigan System; University of Michigan; University of California System; University of California Irvine
  摘要：We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with longer memory than those considered in the current literature. We show that several commonly used methods for independent observations can be applied to the temporally dependent data. In particular, the rates of convergence are obtained for the generalized thr...
• PROJECTED SPLINE ESTIMATION OF THE NONPARAMETRIC FUNCTION IN HIGH-DIMENSIONAL PARTIALLY LINEAR MODELS FOR MASSIVE DATA AI翻译
  作者：Lian, Heng; Zhao, Kaifeng; Lv, Shaogao
  作者单位：City University of Hong Kong; Philips; Philips Research; Nanjing Audit University
  摘要：In this paper, we consider the local asymptotics of the nonparametric function in a partially linear model, within the framework of the divide-and-conquer estimation. Unlike the fixed-dimensional setting in which the parametric part does not affect the nonparametric part, the high-dimensional setting makes the issue more complicated. In particular, when a sparsity-inducing penalty such as lasso is used to make the estimation of the linear part feasible, the bias introduced will propagate to th...
• SEMI-SUPERVISED INFERENCE: GENERAL THEORY AND ESTIMATION OF MEANS AI翻译
  作者：Zhang, Anru; Brown, Lawrence D.; Cai, T. Tony
  作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Pennsylvania
  摘要：We propose a general semi-supervised inference framework focused on the estimation of the population mean. As usual in semi-supervised settings, there exists an unlabeled sample of covariate vectors and a labeled sample consisting of covariate vectors along with real-valued responses (labels). Otherwise, the formulation is assumption-lean in that no major conditions are imposed on the statistical or functional form of the data. We consider both the ideal semi-supervised setting where infinitel...
• CANONICAL CORRELATION COEFFICIENTS OF HIGH-DIMENSIONAL GAUSSIAN VECTORS: FINITE RANK CASE AI翻译
  作者：Bao, Zhigang; Hu, Jiang; Pan, Guangming; Zhou, Wang
  作者单位：Hong Kong University of Science & Technology; Northeast Normal University - China; Nanyang Technological University; National University of Singapore
  摘要：Consider a Gaussian vector z = (x', y')', consisting of two sub-vectors x and y with dimensions p and q, respectively. With n independent observations of z, we study the correlation between x and y, from the perspective of the canonical correlation analysis. We investigate the high-dimensional case: both p and q are proportional to the sample size n. Denote by Sigma(uv) the population cross-covariance matrix of random vectors u and v, and denote by Suv the sample counterpart. The canonical cor...
• 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...
• TEST FOR HIGH-DIMENSIONAL CORRELATION MATRICES AI翻译
  作者：Zheng, Shurong; Cheng, Guanghui; Guo, Jianhua; Zhu, Hongtu
  作者单位：Northeast Normal University - China; Northeast Normal University - China; Guangzhou University; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine
  摘要：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. ...
• UNIFORM PROJECTION DESIGNS AI翻译
  作者：Sun, Fasheng; Wang, Yaping; Xu, Hongquan
  作者单位：Northeast Normal University - China; Northeast Normal University - China; East China Normal University; University of California System; University of California Los Angeles
  摘要：Efficient designs are in high demand in practice for both computer and physical experiments. Existing designs (such as maximin distance designs and uniform designs) may have bad low-dimensional projections, which is undesirable when only a few factors are active. We propose a new design criterion, called uniform projection criterion, by focusing on projection uniformity. Uniform projection designs generated under the new criterion scatter points uniformly in all dimensions and have good space-...
• 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 ...