统计研究
統計研究
통계연구
Statistical Research
2013年
3期
101~105
,共null页
多元正态均值 简单半序约束 极大似然估计 风险函数 PAVA算法
多元正態均值 簡單半序約束 極大似然估計 風險函數 PAVA算法
다원정태균치 간단반서약속 겁대사연고계 풍험함수 PAVA산법
Multivariate Normal Mean; Simple Order Restriction; Maximum Likelihood Estimation; Risk Function; PA VA Algorithm
多元保序回归理论对统计学中研究多维参数在序约束下的估计理论起着关键性作用。本文讨论了当协方差矩阵已知，在简单半序约束下，对三个多元正态总体均值的估计问题，给出了估计的算法。并证明了在多元均方损失条件下，给出的均值估计优于无序约束的均值估计。
多元保序迴歸理論對統計學中研究多維參數在序約束下的估計理論起著關鍵性作用。本文討論瞭噹協方差矩陣已知，在簡單半序約束下，對三箇多元正態總體均值的估計問題，給齣瞭估計的算法。併證明瞭在多元均方損失條件下，給齣的均值估計優于無序約束的均值估計。
다원보서회귀이론대통계학중연구다유삼수재서약속하적고계이론기착관건성작용。본문토론료당협방차구진이지，재간단반서약속하，대삼개다원정태총체균치적고계문제，급출료고계적산법。병증명료재다원균방손실조건하，급출적균치고계우우무서약속적균치고계。
Multivariate isotonic regression theory plays a key role in the study of statistical estimation theory of multivariate parameters under order restriction. In this paper, estimation of the means of three multivariate normal populations under simple order restriction is discussed, while the covariance matrices are known, and corresponding algorithm of estimation is given. It is also demonstrated that, under the condition of generalized square loss, the new estimation of means is better than that under disordered restriction.
