多参数指数族的逆Bhattacharyyà信息阵并应用于正态分布  

THE INVERSE BHATTACHARYYA INFORMATION MATRIX FOR MULTIPARAMETRIC EXPONENTIAL FAMILY AND ITS APPLICATION TO NORMAL DISTRIBUTIONS

作　　者：吴传义[1] 

机构地区：[1]中国科学院系统科学研究所

出　　处：《应用数学学报》1989年第2期205-212,共8页Acta Mathematicae Applicatae Sinica

基　　金：中国科学院科学基金资助的课题

摘　　要：本文进一步讨论多参数指数族中给定可估函数的 UMVUE 的方差计算问题.设定义于(X,B_X)上的 r.v.X 的分布为 P_θ,θ∈Θ.P_θ受某σ-有限测度μ(x)所控,称{P_θ,θ∈Θ)为自然指数族。In this paper,we point out that,for the multiparametric exponential family,any(i,j)-clement of the inverse matrix I_n^(-1) of Bhattacharyyà information matrix with order n has a finitelimit when n→∞.Thus the inverse Bh-matrix is introduced,and it can be given in advance.By using the inverse Bh-matrix it is convenient to calculate the variance of the UMVUE ofsome estimable function.As an example,we give the expression of all elements of the inverseBh-matrix for normal distributions with unknown mean and variance.

关 键 词：多参数指数族 Bh-信息阵 正态分布 

分 类 号：O212.2[理学—概率论与数理统计]