多个正态总体均值与标准差比在简单树序约束下的最大似然估计  

Maximum Likelihood Estimation of Ratios of Means and Standard Deviations from Normal Populations under Tree-order Restriction

作　　者：姬永刚[1] 李树有[1] 赵世舜[2] 史海芳[2] 

机构地区：[1]辽宁工业大学数理科学系,辽宁锦州121001 [2]吉林大学数学学院,吉林长春130012

出　　处：《吉林大学学报（理学版）》2008年第5期829-835,共7页Journal of Jilin University:Science Edition

基　　金：辽宁省教育厅科研基金(批准号:20060409)

摘　　要：考虑k(k>3)个正态总体均值与标准差(均值和标准差均未知)之比在简单树序约束下最大似然估计的求解问题,应用保序回归理论给出了计算均值和标准差最大似然估计的迭代算法,并证明了所给迭代算法是收敛的,给出了k=7时利用迭代算法的模拟结果.For k normal populations with unknown means μi and variances σ^2i〉 0 （i=1,2,…, k） , it is assumed that there is a tree-order restriction between ratios of means and standard deviations. According to the method of isotonic regression, a procedure of obtaining the maximum likelihood estimators of μi＇s and σi＇s under the tree-order restrictions is proposed. In the case of k=7, some connected results and simulation results are given.

关 键 词：简单树序 最大似然估计 似然函数 迭代算法 

分 类 号：O212.1[理学—概率论与数理统计]