【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.更多还原

【Abstract】 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:θ₁≤θ₂≤…≤θ_k and Λ₁≥Λ₂≥…≥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.更多还原