6期

最新文章

• MINIMAX SPARSE PRINCIPAL SUBSPACE ESTIMATION IN HIGH DIMENSIONS AI翻译
  作者：Vu, Vincent Q.; Lei, Jing
  作者单位：University System of Ohio; Ohio State University; Carnegie Mellon University
  摘要：We study sparse principal components analysis in high dimensions, where p (the number of variables) can be much larger than n (the number of observations), and analyze the problem of estimating the subspace spanned by the principal eigenvectors of the population covariance matrix. We introduce two complementary notions of eq subspace sparsity: row sparsity and column sparsity. We prove nonasymptotic lower and upper bounds on the minimax subspace estimation error for 0 <= q <= I. The bounds are...
• A COMPLEMENTARY SET THEORY FOR QUATERNARY CODE DESIGNS AI翻译
  作者：Mukerjee, Rahul; Tang, Boxin
  作者单位：Indian Institute of Management (IIM System); Indian Institute of Management Calcutta; Simon Fraser University
  摘要：Quaternary code (QC) designs form an attractive class of nonregular factorial fractions. We develop a complementary set theory for characterizing optimal QC designs that are highly fractionated in the sense of accommodating a large number of factors. This is in contrast to existing theoretical results which work only for a relatively small number of factors. While the use of imaginary numbers to represent the Gray map associated with QC designs facilitates the derivation, establishing a link w...
• TESTS ALTERNATIVE TO HIGHER CRITICISM FOR HIGH-DIMENSIONAL MEANS UNDER SPARSITY AND COLUMN-WISE DEPENDENCE AI翻译
  作者：Zhong, Ping-Shou; Chen, Song Xi; Xu, Minya
  作者单位：Michigan State University; Peking University; Peking University; Iowa State University
  摘要：We consider two alternative tests to the Higher Criticism test of Donoho and Jin [Ann. Statist. 32 (2004) 962-994] for high-dimensional means under the sparsity of the nonzero means for sub-Gaussian distributed data with unknown column-wise dependence. The two alternative test statistics are constructed by first thresholding L-1 and L-2 statistics based on the sample means, respectively, followed by maximizing over a range of thresholding levels to make the tests adaptive to the unknown signal...
• UNEXPECTED PROPERTIES OF BANDWIDTH CHOICE WHEN SMOOTHING DISCRETE DATA FOR CONSTRUCTING A FUNCTIONAL DATA CLASSIFIER AI翻译
  作者：Carroll, Raymond J.; Delaigle, Aurore; Hall, Peter
  作者单位：Texas A&M University System; Texas A&M University College Station; University of Melbourne
  摘要：The data functions that are studied in the course of functional data analysis are assembled from discrete data, and the level of smoothing that is used is generally that which is appropriate for accurate approximation of the conceptually smooth functions that were not actually observed. Existing literature shows that this approach is effective, and even optimal, when using functional data methods for prediction or hypothesis testing. However, in the present paper we show that this approach is ...
• GAUSSIAN GRAPHICAL MODEL ESTIMATION WITH FALSE DISCOVERY RATE CONTROL AI翻译
  作者：Liu, Weidong
  作者单位：Shanghai Jiao Tong University; Shanghai Jiao Tong University
  摘要：This paper studies the estimation of a high-dimensional Gaussian graphical model (GGM). Typically, the existing methods depend on regularization techniques. As a result, it is necessary to choose the regularized parameter. However, the precise relationship between the regularized parameter and the number of false edges in GGM estimation is unclear. In this paper we propose an alternative method by a multiple testing procedure. Based on our new test statistics for conditional dependence, we pro...
• ACTIVE SEQUENTIAL HYPOTHESIS TESTING AI翻译
  作者：Naghshvar, Mohammad; Javidi, Tara
  作者单位：Qualcomm; University of California System; University of California San Diego
  摘要：Consider a decision maker who is responsible to dynamically collect observations so as to enhance his information about an underlying phenomena of interest in a speedy manner while accounting for the penalty of wrong declaration. Due to the sequential nature of the problem, the decision maker relies on his current information state to adaptively select the most informative sensing action among the available ones. In this paper, using results in dynamic programming, lower bounds for the optimal...
• SPARSE PCA: OPTIMAL RATES AND ADAPTIVE ESTIMATION AI翻译
  作者：Cai, T. Tony; Ma, Zongming; Wu, Yihong
  作者单位：University of Pennsylvania; University of Illinois System; University of Illinois Urbana-Champaign
  摘要：Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional setting. Under mild technical conditions, we first establish the optimal rates of convergence for estimating the principal subspace which are sharp with respect to all the parameters, thus providing a complete characterization of the difficulty of the estimation p...
• GAUSSIAN APPROXIMATIONS AND MULTIPLIER BOOTSTRAP FOR MAXIMA OF SUMS OF HIGH-DIMENSIONAL RANDOM VECTORS AI翻译
  作者：Chernozhukov, Victor; Chetverikov, Denis; Kato, Kengo
  作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); University of California System; University of California Los Angeles; University of Tokyo
  摘要：We derive a Gaussian approximation result for the maximum of a sum of high-dimensional random vectors. Specifically, we establish conditions under which the distribution of the maximum is approximated by that of the maximum of a sum of the Gaussian random vectors with the same covariance matrices as the original vectors. This result applies when the dimension of random vectors (p) is large compared to the sample size (n); in fact, p can be much larger than n, without restricting correlations o...
• COVARIANCE AND PRECISION MATRIX ESTIMATION FOR HIGH-DIMENSIONAL TIME SERIES AI翻译
  作者：Chen, Xiaohui; Xu, Mengyu; Wu, Wei Biao
  作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University of Chicago
  摘要：We consider estimation of covariance matrices and their inverses (a.k.a. precision matrices) for high-dimensional stationary and locally stationary time series. In the latter case the covariance matrices evolve smoothly in time, thus forming a covariance matrix function. Using the functional dependence measure of Wu [Proc. Natl. Acad. Sci. USA 102 (2005) 14150-14154 (electronic)], we obtain the rate of convergence for the thresholded estimate and illustrate how the dependence affects the rate ...
• STRUCTURE ESTIMATION FOR DISCRETE GRAPHICAL MODELS: GENERALIZED COVARIANCE MATRICES AND THEIR INVERSES AI翻译
  作者：Loh, Po-Ling; Wainwright, Martin J.
  作者单位：University of California System; University of California Berkeley
  摘要：We investigate the relationship between the structure of a discrete graphical model and the support of the inverse of a generalized covariance matrix. We show that for certain graph structures, the support of the inverse covariance matrix of indicator variables on the vertices of a graph reflects the conditional independence structure of the graph. Our work extends results that have previously been established only in the context of multivariate Gaussian graphical models, thereby addressing an...