基于简单半序约束条件下k个多元正态总体的均值估计  

Estimation of the Means for k Multivariate Normal Populations Based on Simple Partial Order Restriction

作　　者：罗平 李树有[2] 吴纯杰[3] LUO PING;LI SHUYOU;WU CHUNJIE(Department of Statistics,Shanghai University of Finance and Economics Zhejiang College,Digital Intelligence Management Research Institute,Jinhua 321000,China;College of Science,Liaoning University of Technology,Jinzhou 121000,China;School of Statistics and Data Science,Shanghai University of Finance and Economics,Shanghai 200433,China)

机构地区：[1]上海财经大学浙江学院统计系,数智管理研究院,金华321000 [2]辽宁工业大学理学院,锦州121000 [3]上海财经大学统计与数据科学学院,上海200433

出　　处：《应用数学学报》2025年第2期195-207,共13页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金面上项目(11871324)资助。

摘　　要：在特定实际问题中,含有序和不等式约束的结构在多个领域中都有着广泛的应用.在计算这类参数的估计时,通常会受到序约束条件的限制.例如,在药物检验中,研究人员可能对某个药物的剂量进行限制,因此需要考虑序约束条件.因此,序约束均值估计在这些应用中具有重要的应用价值.在以往的文献中,关于序约束下均值估计问题集中在2个和3个多元正态总体,本文在此基础上进行拓展,研究了k个多元正态总体均值在简单半序约束下的估计问题,提出总体协方差矩阵Σ_(i)已知时总体均值基于PAVA算法的一种新估计μ,并证明了它一致优于无序约束下的极大似然估计X.最后通过模拟实验验证了新估计方法的有效性,并与极大似然估计方法进行了比较.In specific practical problems,structures with ordered and inequality constraints find extensive applications in multiple fields.When estimating parameters in such cases,one often encounters restrictions imposed by ordered constraints.For instance,in pharmaceutical testing,researchers may impose constraints on the dosage of a particular drug,necessitating consideration of ordered constraints.Therefore,ordered constraint mean estimation holds significant practical value in these applications.In previous literature,the focus on mean estimation under ordered constraints has been mainly on 2 and 3 multivariate normal populations.This paper extends this focus to the estimation problem of k multivariate normal population means under simple partial order constraints.It introduces a new estimate μ,based on the PAVA algorithm when the population covariance matrix ∑_(i) is known,and proves its consistent superiority over the unordered maximum likelihood estimate X.Finally,the effectiveness of the proposed estimation method is validated through simulation experiments and compared with the maximum likelihood estimation method.

关 键 词：k个多元正态分布 简单半序约束 极大似然估计 风险函数 PAVA算法 

分 类 号：O212.7[理学—概率论与数理统计]