-
作者：Mukherjee, Gourab; Johnstone, Iain M.
作者单位：University of Southern California; Stanford University
摘要：We consider estimating the predictive density under Kullback-Leibler loss in an l(0) sparse Gaussian sequence model. Explicit expressions of the first order minimax risk along with its exact constant, asymptotically least favorable priors and optimal predictive density estimates are derived. Compared to the sparse recovery results involving point estimation of the normal mean, new decision theoretic phenomena are seen. Suboptimal performance of the class of plug-in density estimates reflects t...
-
作者：Kong, Xin-Bing; Liu, Zhi; Jing, Bing-Yi
作者单位：Soochow University - China; Soochow University - China; University of Macau; Hong Kong University of Science & Technology
摘要：Pure-jump processes have been increasingly popular in modeling high-frequency financial data, partially due to their versatility and flexibility. In the meantime, several statistical tests have been proposed in the literature to check the validity of using pure-jump models. However, these tests suffer from several drawbacks, such as requiring rather stringent conditions and having slow rates of convergence. In this paper, we propose a different test to check whether the underlying process of h...
-
作者：Liu, Haoyang; Aue, Alexander; Paul, Debashis
作者单位：University of California System; University of California Berkeley; University of California System; University of California Davis
摘要：This paper is concerned with extensions of the classical Marcenko-Pastur law to time series. Specifically, p-dimensional linear processes are considered which are built from innovation vectors with independent, identically distributed (real- or complex-valued) entries possessing zero mean, unit variance and finite fourth moments. The coefficient matrices of the linear process are assumed to be simultaneously diagonalizable. In this setting, the limiting behavior of the empirical spectral distr...
-
作者：Cai, T. Tony; Zhang, Anru
作者单位：University of Pennsylvania
摘要：Estimation of low-rank matrices is of significant interest in a range of contemporary applications. In this paper, we introduce a rank-one projection model for low-rank matrix recovery and propose a constrained nuclear norm minimization method for stable recovery of low-rank matrices in the noisy case. The procedure is adaptive to the rank and robust against small perturbations. Both upper and lower bounds for the estimation accuracy under the Frobenius norm loss are obtained. The proposed est...
-
作者：Brownlees, Christian; Joly, Emilien; Lugosi, Gabor
作者单位：Pompeu Fabra University; ICREA; Pompeu Fabra University; Pompeu Fabra University
摘要：The purpose of this paper is to discuss empirical risk minimization when the losses are not necessarily bounded and may have a distribution with heavy tails. In such situations, usual empirical averages may fail to provide reliable estimates and empirical risk minimization may provide large excess risk. However, some robust mean estimators proposed in the literature may be used to replace empirical means. In this paper, we investigate empirical risk minimization based on a robust estimate prop...
-
作者：Spokoiny, Vladimir; Zhilova, Mayya
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Humboldt University of Berlin; Moscow Institute of Physics & Technology; Russian Academy of Sciences; HSE University (National Research University Higher School of Economics)
摘要：A multiplier bootstrap procedure for construction of likelihood-based confidence sets is considered for finite samples and a possible model misspecification. Theoretical results justify the bootstrap validity for a small or moderate sample size and allow to control the impact of the parameter dimension p: the bootstrap approximation works if p(3)/n is small. The main result about bootstrap validity continues to apply even if the underlying parametric model is misspecified under the so-called s...
-
作者：Castillo, Ismael
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
-
作者：Mai, Qing; Zou, Hui
作者单位：State University System of Florida; Florida State University; University of Minnesota System; University of Minnesota Twin Cities
摘要：A new model-free screening method called the fused Kolmogorov filter is proposed for high-dimensional data analysis. This new method is fully nonparametric and can work with many types of covariates and response variables, including continuous, discrete and categorical variables. We apply the fused Kolmogorov filter to deal with variable screening problems emerging from a wide range of applications, such as multiclass classification, nonparametric regression and Poisson regression, among other...
-
作者：Yang, Yanrong; Pan, Guangming
作者单位：Monash University; Nanyang Technological University
摘要：This paper proposes a new statistic to test independence between two high dimensional random vectors X: p(1) x 1 and Y : p(2) x 1. The proposed statistic is based on the sum of regularized sample canonical correlation coefficients of X and Y. The asymptotic distribution of the statistic under the null hypothesis is established as a corollary of general central limit theorems (CLT) for the linear statistics of classical and regularized sample canonical correlation coefficients when p(1) and p(2...
-
作者：Bao, Zhigang; Pan, Guangming; Zhou, Wang
作者单位：Zhejiang University; Nanyang Technological University; National University of Singapore
摘要：This paper is aimed at deriving the universality of the largest eigenvalue of a class of high-dimensional real or complex sample covariance matrices of the form W-N = Sigma(XX)-X-1/2*E-1/2. Here, X = (xij)(M,N) is an M x N random matrix with independent entries x(ij), 1 <= i <= M, 1 <= j <= N such that Ex(ij) = 0, E vertical bar x(ij)vertical bar(2) = 1/N. On dimensionality, we assume that M = M(N) and N/M -> d is an element of(0, infinity) as N -> infinity. For a class of general deterministi...
