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Nearly optimal Bayesian shrinkage for high-dimensional regression

Science China Mathematics 2023年第2期66卷 409-442页

作者： Qifan Song Faming Liang Department of Statistics Purdue UniversityWest LafayetteIN 47906USA

During the past decade,shrinkage priors have received much attention in Bayesian analysis of high-dimensional *** paper establishes the posterior consistency for high-dimensional linear regression with a class of shrinkage priors,which has a heavy and flat tail and allocates a sufficiently large probability mass in a very small neighborhood of *** enjoying its efficiency in posterior simulations,the shrinkage prior can lead to a nearly optimal posterior contraction rate and the variable selection consistency as the spike-and-slab *** numerical results show that under the posterior consistency,Bayesian methods can yield much better results in variable selection than the regularization methods such as LASSO and *** paper also establishes a BvM-type result,which leads to a convenient way of uncertainty quantification for regression coefficient estimates.

关键词： Bayesian variable selection absolutely continuous shrinkage prior heavy tail posterior consistency high-dimensional inference

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Variable Selection in high-dimensional Error-in-Variables Models via Controlling the False Discovery Proportion

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Communications in Mathematics and Statistics 2022年第1期10卷 123-151页

作者： Xudong Huang Nana Bao Kai Xu Guanpeng Wang School of Mathematics and Statistics Anhui Normal University189 South Jiuhua RoadWuhu 241002AnhuiPeople’s Republic of China School of Mathematical Sciences Capital Normal University105 West Third Ring RoadBeijing 100048People’s Republic of China

Multiple testing has gained much attention in high-dimensional statistical theory and applications,and the problem of variable selection can be regarded as a generalization of the multiple *** is aiming to select the important variables among many *** variable selection in high-dimensional linear models with measurement errors is *** the influence of high-dimensional parameters and measurement errors need to be considered to avoid severely *** consider the problem of variable selection in error-in-variables and introduce the DCoCoLasso-FDP procedure,a new variable selection *** constructing the consistent estimator of false discovery proportion(FDP)and false discovery rate(FDR),our method can prioritize the important variables and control FDP and FDR at a specifical level in error-in-variables *** extensive simulation study is conducted to compare DCoCoLasso-FDP procedure with existing methods in various settings,and numerical results are provided to present the efficiency of our method.

关键词： Multiple testing high-dimensional inference False discovery proportion Measurement error models Variable selection

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Science China Mathematics 2024年第2期67卷 405-430页

作者： Junzhuo Gao Lei Wang Heng Lian School of Statistics and Data Science&LPMC Nankai UniversityTianjin 300071China Department of Mathematics City University of Hong KongHong KongChina

In this paper, we consider the unified optimal subsampling estimation and inference on the lowdimensional parameter of main interest in the presence of the nuisance parameter for low/high-dimensionalgeneralized linear models (GLMs) with massive data. We first present a general subsampling decorrelated scorefunction to reduce the influence of the less accurate nuisance parameter estimation with the slow convergencerate. The consistency and asymptotic normality of the resultant subsample estimator from a general decorrelatedscore subsampling algorithm are established, and two optimal subsampling probabilities are derived under theA- and L-optimality criteria to downsize the data volume and reduce the computational burden. The proposedoptimal subsampling probabilities provably improve the asymptotic efficiency of the subsampling schemes in thelow-dimensional GLMs and perform better than the uniform subsampling scheme in the high-dimensional GLMs.A two-step algorithm is further proposed to implement, and the asymptotic properties of the correspondingestimators are also given. Simulations show satisfactory performance of the proposed estimators, and twoapplications to census income and Fashion-MNIST datasets also demonstrate its practical applicability.

关键词： A-optimality decorrelated score subsampling high-dimensional inference L-optimality massive data

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