Admissible predictive density estimation
Admissible predictive density estimation
复制标题
可接受的预测密度估计
DOI：
10.1214/07-aos506
复制
发表时间：
2008
影响因子：
4.5
通讯作者：
Xinyi Xu
中科院分区：
文献类型：
--
作者：
L. Brown;E. George;Xinyi Xu
设XjNp（; vxI）和YjNp（; vyI）是具有共同未知均值的独立p维多元正态向量。在观测X = x的基础上，考虑了在期望Kullback-Leibler损失下估计Y的真预测密度p（yj）的问题.这里我们的重点是这个问题的可受理程序的表征。我们证明了所有广义贝叶斯规则的类是一个完备类，并且Brown和Hwang（1982）的易于解释的条件对于形式贝叶斯规则是可容许的是足够的。1.导论.设Xj Np（;v xI）和Yj Np（;v yI）是具有共同未知均值2 Rp的独立p维多元正态向量。我们假设vx > 0和vy > 0是已知的。我们让p（xj）和p（yj）表示X和Y的条件密度，在整个过程中抑制对vx和vy的依赖。在只观察X = x的基础上，我们考虑估计Y的密度p（yj）的问题。自然作用空间A_0由R_p上的所有真密度组成，即：
Let Xj Np(;v xI) and Y j Np(;v yI) be independent p-dimensional multivariate normal vectors with common unknown mean . Based on observing X = x, we consider the problem of estimating the true predictive density p(yj ) of Y under expected Kullback-Leibler loss. Our focus here is the characterization of admissible procedures for this problem. We show that the class of all generalized Bayes rules is a complete class, and that the easily interpretable conditions of Brown and Hwang (1982) are sucient for a formal Bayes rule to be admissible. 1. Introduction. Let Xj Np(;v xI) and Yj Np(;v yI) be independent p-dimensional multivariate normal vectors with a common unknown mean 2 R p . We assume that vx > 0 and vy > 0 are known. We let p(xj ) and p(yj ) denote the conditional densities of X and Y , suppressing the dependence onvx and vy throughout. Based on observing only X = x, we consider the problem of estimating the density p(yj ) of Y . The natural action spaceA0 consists of all proper densities on R p , i.e.