2013

最新文章

• 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...
• CENTRAL LIMIT THEOREMS FOR CLASSICAL LIKELIHOOD RATIO TESTS FOR HIGH-DIMENSIONAL NORMAL DISTRIBUTIONS AI翻译
  作者：Jiang, Tiefeng; Yang, Fan
  作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Minnesota System; University of Minnesota Twin Cities
  摘要：For random samples of size n obtained from p-variate normal distributions, we consider the classical likelihood ratio tests (LRT) for their means and covariance matrices in the high-dimensional setting. These test statistics have been extensively studied in multivariate analysis, and their limiting distributions under the null hypothesis were proved to be chi-square distributions as n goes to infinity and p remains fixed. In this paper, we consider the high-dimensional case where both p and n ...
• TESTS FOR COVARIANCE MATRIX WITH FIXED OR DIVERGENT DIMENSION AI翻译
  作者：Zhang, Rongmao; Peng, Liang; Wang, Ruodu
  作者单位：Zhejiang University; University System of Georgia; Georgia Institute of Technology; University of Waterloo
  摘要：Testing covariance structure is of importance in many areas of statistical analysis, such as microarray analysis and signal processing. Conventional tests for finite-dimensional covariance cannot be applied to high-dimensional data in general, and tests for high-dimensional covariance in the literature usually depend on some special structure of the matrix. In this paper, we propose some empirical likelihood ratio tests for testing whether a covariance matrix equals a given one or has a banded...
• RATES OF CONVERGENCE OF THE ADAPTIVE LASSO ESTIMATORS TO THE ORACLE DISTRIBUTION AND HIGHER ORDER REFINEMENTS BY THE BOOTSTRAP AI翻译
  作者：Chatterjee, A.; Lahiri, S. N.
  作者单位：Indian Statistical Institute; Indian Statistical Institute Delhi; North Carolina State University
  摘要：Zou [J. Amer. Statist. Assoc. 101 (2006) 1418-1429] proposed the Adaptive LASSO (ALASSO) method for simultaneous variable selection and estimation of the regression parameters, and established its oracle property. In this paper, we investigate the rate of convergence of the ALASSO estimator to the oracle distribution when the dimension of the regression parameters may grow to infinity with the sample size. It is shown that the rate critically depends on the choices of the penalty parameter and...
• MAXIMUM-LIKELIHOOD ESTIMATION FOR DIFFUSION PROCESSES VIA CLOSED-FORM DENSITY EXPANSIONS AI翻译
  作者：Li, Chenxu
  作者单位：Peking University
  摘要：This paper proposes a widely applicable method of approximate maximum-likelihood estimation for multivariate diffusion process from discretely sampled data. A closed-form asymptotic expansion for transition density is proposed and accompanied by an algorithm containing only basic and explicit calculations for delivering any arbitrary order of the expansion. The likelihood function is thus approximated explicitly and employed in statistical estimation. The performance of our method is demonstra...
• EXACT SAMPLING AND COUNTING FOR FIXED-MARGIN MATRICES AI翻译
  作者：Miller, Jeffrey W.; Harrison, Matthew T.
  作者单位：Brown University
  摘要：The uniform distribution on matrices with specified row and column sums is often a natural choice of null model when testing for structure in two-way tables (binary or nonnegative integer). Due to the difficulty of sampling from this distribution, many approximate methods have been developed. We will show that by exploiting certain symmetries, exact sampling and counting is in fact possible in many nontrivial real-world cases. We illustrate with real datasets including ecological co-occurrence...
• LEARNING LOOPY GRAPHICAL MODELS WITH LATENT VARIABLES: EFFICIENT METHODS AND GUARANTEES AI翻译
  作者：Anandkumar, Animashree; Valluvan, Ragupathyraj
  作者单位：University of California System; University of California Irvine
  摘要：The problem of structure estimation in graphical models with latent variables is considered. We characterize conditions for tractable graph estimation and develop efficient methods with provable guarantees. We consider models where the underlying Markov graph is locally tree-like, and the model is in the regime of correlation decay. For the special case of the Ising model, the number of samples n required for structural consistency of our method scales as n = Omega(theta(-delta eta(eta+1)-2)(m...
• NONPARAMETRIC REGRESSION WITH THE SCALE DEPENDING ON AUXILIARY VARIABLE AI翻译
  作者：Efromovich, Sam
  作者单位：University of Texas System; University of Texas Dallas
  摘要：The paper is devoted to the problem of estimation of a univariate component in a heteroscedastic nonparametric multiple regression under the mean integrated squared error (MISE) criteria. The aim is to understand how the scale function should be used for estimation of the univariate component. It is known that the scale function does not affect the rate of the MISE convergence, and as a result sharp constants are explored. The paper begins with developing a sharp-minimax theory for a pivotal m...
• MULTIVARIATE DENSITY ESTIMATION UNDER SUP-NORM LOSS: ORACLE APPROACH, ADAPTATION AND INDEPENDENCE STRUCTURE AI翻译
  作者：Lepski, Oleg
  作者单位：Aix-Marseille Universite
  摘要：This paper deals with the density estimation on R-d under sup-norm loss. We provide a fully data-driven estimation procedure and establish for it a so-called sup-norm oracle inequality. The proposed estimator allows us to take into account not only approximation properties of the underlying density, but eventual independence structure as well. Our results contain, as a particular case, the complete solution of the bandwidth selection problem in the multivariate density model. Usefulness of the...
• 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 ...