论文标题
在贝叶斯案中，多元正常平均值的收缩估计量的最小程度和风险限制的限制
Minimaxity and Limits of Risks Ratios of Shrinkage Estimators of a Multivariate Normal Mean in the Bayesian Case
论文作者
论文摘要
在本文中，我们考虑了多变量正态分布的平均$θ$的两种形式的收缩估计器$ x \ sim n_ {p} \ left（θ，σ^{2} i_ {p} i_ {p} \ right）$，其中$σ^{2} $是未知的。我们采用先前的定律$θ\ sim n_ {p} \ left（\ upsilon，τ^{2} i_ {p} \ right）$，我们构成了修改的贝叶斯估算值$Δ_{b}^{b}^{\ ast} $ and ebesifialical modifical modifialical modification bayes estator usevator $Δ__}我们有兴趣研究这些估计量的最小值和风险比的极限，与$ n $ and $ p $无限时的最大似然估计器$ x $。
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.
