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作者：Scornet, Erwan; Biau, Gerard; Vert, Jean-Philippe
作者单位：Sorbonne Universite; Universite PSL; MINES ParisTech; UNICANCER; Universite PSL; Institut Curie; Universite PSL; UNICANCER; Institut Curie; Institut National de la Sante et de la Recherche Medicale (Inserm)
摘要：Random forests are a learning algorithm proposed by Breiman [Mach. Leant. 45 (2001) 5-32] that combines several randomized decision trees and aggregates their predictions by averaging. Despite its wide usage and outstanding practical performance, little is known about the mathematical properties of the procedure. This disparity between theory and practice originates in the difficulty to simultaneously analyze both the randomization process and the highly data-dependent tree structure. In the p...
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作者：Bao, Zhigang; Lin, Liang-Ching; Pan, Guangming; Zhou, Wang
作者单位：Nanyang Technological University; National Cheng Kung University; National University of Singapore
摘要：Let Q = (Qi,...,Qn) be a random vector drawn from the uniform distribution on the set of all n! permutations of {1,2,...,n}. Let Z = (Z1,...,Zn), where Z(j) is the mean zero variance one random variable obtained by centralizing and normalizing Q(j), j = 1,...,n. Assume that X-i, i = 1,...,p are i.i.d. copies of 1 root p Z and X = Xp,n is the p x n random matrix with X-i as its ith row. Then S-n = XX* is called the p x n Spearman's rank correlation matrix which can be regarded as a high dimensi...
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作者：Basu, Sumanta; Michailidis, George
作者单位：University of Michigan System; University of Michigan
摘要：Many scientific and economic problems involve the analysis of high-dimensional time series datasets. However, theoretical studies in high-dimensional statistics to date rely primarily on the assumption of independent and identically distributed (i.i.d.) samples. In this work, we focus on stable Gaussian processes and investigate the theoretical properties of l(1)-regularized estimates in two important statistical problems in the context of high-dimensional time series: (a) stochastic regressio...
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作者：Shang, Zuofeng; Cheng, Guang
作者单位：Purdue University System; Purdue University
摘要：We propose a roughness regularization approach in making nonparametric inference for generalized functional linear models. In a reproducing kernel Hilbert space framework, we construct asymptotically valid confidence intervals for regression mean, prediction intervals for future response and various statistical procedures for hypothesis testing. In particular, one procedure for testing global behaviors of the slope function is adaptive to the smoothness of the slope function and to the structu...
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作者：Vogt, Michael; Dette, Holger
作者单位：University of Konstanz; Ruhr University Bochum
摘要：In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start to change. In many cases, it is of interest to locate the time point where the properties start to vary. In contrast to the analysis of abrupt changes, methods for detecting smooth or gradual change points are less developed and often require strong paramet...
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作者：Sherlock, Chris; Thiery, Alexandre H.; Roberts, Gareth O.; Rosenthal, Jeffrey S.
作者单位：Lancaster University; National University of Singapore; University of Warwick; University of Toronto
摘要：We examine the behaviour of the pseudo-marginal random walk Metropolis algorithm, where evaluations of the target density for the accept/reject probability are estimated rather than computed precisely. Under relatively general conditions on the target distribution, we obtain limiting formulae for the acceptance rate and for the expected squared jump distance, as the dimension of the target approaches infinity, under the assumption that the noise in the estimate of the log-target is additive an...
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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...
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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...
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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...
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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...
