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作者：Zhang, Xianyang; Yao, Shun; Shao, Xiaofeng
作者单位：Texas A&M University System; Texas A&M University College Station; University of Illinois System; University of Illinois Urbana-Champaign
摘要：Motivated by applications in biological science, we propose a novel test to assess the conditional mean dependence of a response variable on a large number of covariates. Our procedure is built on the martingale difference divergence recently proposed in Shao and Zhang [J. Amer. Statist. Assoc. 109 (2014) 1302-1318], and it is able to detect certain type of departure from the null hypothesis of conditional mean independence without making any specific model assumptions. Theoretically, we estab...
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作者：Zheng, Qi; Peng, Limin; He, Xuming
作者单位：University of Louisville; Emory University; University of Michigan System; University of Michigan
摘要：Censored quantile regression (CQR) has emerged as a useful regression tool for survival analysis. Some commonly used CQR methods can be characterized by stochastic integral-based estimating equations in a sequential manner across quantile levels. In this paper, we analyze CQR in a high dimensional setting where the regression functions over a continuum of quantile levels are of interest. We propose a two-step penalization procedure, which accommodates stochastic integral based estimating equat...
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作者：Mousavi, Ali; Maleki, Arian; Baraniuk, Richard G.
作者单位：Rice University; Columbia University
摘要：This paper studies the optimal tuning of the regularization parameter in LASSO or the threshold parameters in approximate message passing (AMP). Considering a model in which the design matrix and noise are zero-mean i.i.d. Gaussian, we propose a data-driven approach for estimating the regularization parameter of LASSO and the threshold parameters in AMP. Our estimates are consistent, that is, they converge to their asymptotically optimal values in probability as n, the number of observations, ...
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作者：Bellec, Pierre C.
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Rutgers University System; Rutgers University New Brunswick; Rutgers University System; Rutgers University New Brunswick
摘要：We study the problem of aggregation of estimators when the estimators are not independent of the data used for aggregation and no sample splitting is allowed. If the estimators are deterministic vectors, it is well known that the minimax rate of aggregation is of order log(M), where M is the number of estimators to aggregate. It is proved that for affine estimators, the minimax rate of aggregation is unchanged: it is possible to handle the linear dependence between the affine estimators and th...
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作者：Leung, Dennis; Drton, Mathias
作者单位：Chinese University of Hong Kong; University of Washington; University of Washington Seattle
摘要：We treat the problem of testing independence between m continuous variables when m can be larger than the available sample size n. We consider three types of test statistics that are constructed as sums or sums of squares of pairwise rank correlations. In the asymptotic regime where both m and n tend to infinity, a martingale central limit theorem is applied to show that the null distributions of these statistics converge to Gaussian limits, which are valid with no specific distributional or m...
