半序约束下两个正态总体均值和协方差阵估计的算法

An Algorithm for Maximum Likelihood Estimation of Mean Vectors and Convariance Matrices from Multivariate Normal Distribution Under Simultaneous Order Restrictions

对给定2个 P 维正态总体,未知均值和协方差阵分别为θ_i和∧_i,i=1,2.本文研究了均值和协方差阵之间都有一个简单半序约束:θ_1≤θ_2,∧_1≥∧_2>0的条件下的估计问题,进而给出了一个求解的迭代方法,并证明其收敛性。

For 2p-multiple normal population with unknown mean vector θ_i and unknon convariance matrix Λ_i,i=1,2,assure that there are some order restrictions among the mean vectors and convariance matrixes respectively.For example:Simple order restrictions:θ≤θ_2,Λ_1≥Λ_2> O.An algorithm for maximum likelihood estimations of θ_is and Λ_is proposed and its conver- gence is proved.