去偏收缩估计量的非极小极大性

Minimaxity and Limits of Risks Ratios of Shrinkage Estimators of a Multivariate Normal Mean in the Bayesian Case

In this article, we consider two forms of shrinkage estimators of the mean $θ$ of a multivariate normal distribution $X\sim N_{p}\left(θ, σ^{2}I_{p}\right)$ where $σ^{2}$ is unknown. We take the prior law $θ\sim N_{p}\left(\upsilon, τ^{2}I_{p}\right)$ and we constuct a Modified Bayes estimator $δ_{B}^{\ast}$ and an Empirical Modified Bayes estimator $δ_{EB}^{\ast}$. We are interested in studying the minimaxity and the limits of risks ratios of these estimators, to the maximum likelihood estimator $X$, when $n$ and $p$ tend to infinity.

l_p-norm based James-Stein estimation with minimaxity and sparsity

A new class of minimax Stein-type shrinkage estimators of a multivariate normal mean is studied where the shrinkage factor is based on an l_p norm. The proposed estimators allow some but not all coordinates to be estimated by 0 thereby allow sparsity as well as minimaxity.

使用单组收缩先验进行多重检验的渐近极小化极大最优性

Sharp Asymptotic Minimaxity for Multiple Testing Using One-Group Shrinkage Priors

研究稀疏高斯序列模型中基于全局-局部尺度混合正态先验的贝叶斯多重检验规则的渐近极小化极大性质，证明在已知或未知稀疏度下，适当选择全局收缩参数可使检验规则达到精确极小化极大风险。

Bayesian Shrinkage towards Sharp Minimaxity

Shrinkage prior are becoming more and more popular in Bayesian modeling for high dimensional sparse problems due to its computational efficiency. Recent works show that a polynomially decaying prior leads to satisfactory posterior asymptotics under regression models. In the literature, statisticians have investigated how the global shrinkage parameter, i.e., the scale parameter, in a heavy tail prior affects the posterior contraction. In this work, we explore how the shape of the prior, or more specifically, the polynomial order of the prior tail affects the posterior. We discover that, under …

分层计数数据的贝叶斯收缩估计

Bayesian Shrinkage Estimation for Stratified Count Data

针对含聚合辅助信息的分层 Poisson 计数数据，本文基于共轭先验构造贝叶斯收缩估计量，比较其与直接估计量的风险，给出占优条件并证明极小极大性与容许性。

Asymptotic Minimaxity, Optimal Posterior Concentration and Asymptotic Bayes Optimality of Horseshoe-type Priors Under Sparsity

In this article, we investigate certain asymptotic optimality properties of a very broad class of one-group continuous shrinkage priors for simultaneous estimation and testing of a sparse normal mean vector. Asymptotic optimality of Bayes estimates and posterior concentration properties corresponding to the general class of one-group priors under consideration are studied where the data is assumed to be generated according to a multivariate normal distribution with a fixed unknown mean vector. Under the assumption that the number of non-zero means is known, we show that Bayes estimators arisin…