半序约束下多维正态总体均值和协方差阵的最大似然估计  

Maximum Likelihood Estimation of Mean Vectors and Covariance Matrices from Multivariate Normal Distribution under Simultaneous Order Restrictions

作　　者：李树有[1] 史宁中[2] 张宝学[2] 

机构地区：[1]辽宁工学院数理科学系 [2]东北师范大学数学系,吉林长春130024

出　　处：《应用数学》2005年第3期397-403,共7页Mathematica Applicata

基　　金：辽宁省自然科学基金赞助项目(20031066)

摘　　要：对给定K个P维正态总体,未知均值和协方差阵分别为θi和Λi,i=1,2,…,k,本文考虑均值和协方差阵之间都在一个简单半序约束θ1≤θ2≤…≤θk,Λ1≥Λ2≥…≥Λk>0条件下的估计问题.讨论θi和Λi的最大似然估计的性质,并给出一个求解的迭代方法.For kp-multiple normal populations with unknown mean vector θ_i and unknown covariance matrix Λ_i,i=1,2,…,k,assume that there are some order restrictions among the mean vectors and covariance matrices,respectively,for example,simple order restrictions:θ_1≤θ_2≤…≤θ_k and Λ_1≥Λ_2≥…≥Λ_k>0.Some properties of maximum likelihood estimations of θ′_is and Λ′_is are discussed and an algorithm of obstaining the maximum likelihood estimators under the order restriction is proposed.

关 键 词：最大似然估计 保序回归 迭代算法 

分 类 号：O212.1[理学—概率论与数理统计]