多元正态分布熵的Stein型和Brester-Zidek型估计  

Stein-type and Brewster-Zidek-type Estimators of Entropy of a Multivariate Normal Distribution

作　　者：王理峰[1] Wang Lifeng(Department of Mathematics,Nanjing Institute of Railway Technology,Nanjing 210031,China)

机构地区：[1]南京铁道职业技术学院数学系,南京210031

出　　处：《统计与决策》2020年第8期16-20,共5页Statistics & Decision

基　　金：江苏省高校哲学社会科学研究指导项目(2014SJD283)。

摘　　要：基于一些随机样本,在Linex损失下估计期望及方差阵都未知的多元正态分布的熵。在仅依赖于|S|的估计类中,熵的最优仿射同变估计δc*是可容许估计,但在一些范围更大的估计类中,δc*是不可容许估计。文章首先用Stein型估计δ?ST去改进δc*,但Stein型估计不是光滑的,然后用具有光滑性的Brester-Zidek型估计去改进δc*,进一步研究知Brester-Zidek估计是可容许估计,也是Bayes估计。Based on a random sample,this paper estimates the entropy of a multivariate normal distribution with unknown expectation and variance matrices under Linex loss function.In the class of estimators that depend on|S|alone,the optimal affine equivariant estimator of entropyδc*is admissible,but in some larger estimator classes,δc*is an inadmissible estimate.This paper firstly uses Stein-type estimatorδ?ST to improveδc*,but the Stein-type estimator is non-smooth.Then the paper uses the Brewster-Zidek-type estimator with smoothness to improveδc*.Further studies show that the Brewster-Zidek-type estimator is an admissible estimator and also a Bayes estimator.

关 键 词：多元正态分布 熵 LINEX损失 Stein型估计 Brester-Zidek型估计 Bayes估计 可容许估计 

分 类 号：O212.4[理学—概率论与数理统计]