增长曲线模型中一致最小风险无偏估计的存在性  

THE EXISTENCE OF UNIFORMLY MINIMUM RISK UNBIASED ESTIMATORS IN GROWTH CURVE MODELS

作　　者：吴启光[1] 冯泰[2] 

机构地区：[1]中国科学院系统科学研究所,北京100080 [2]中央广播电视大学,北京100031

出　　处：《系统科学与数学》1998年第1期68-77,共10页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金

摘　　要：考虑协方差阵任意，或具有均匀协方差结构，或具有序列协方差结构的正态增长曲线模型本文将文[19]在设计矩阵满秩，且仅估计回归系数矩阵的情形获得的结果推广到设计矩阵不必列满秩，且同时估计回归系数矩阵的线性可估函数和协方差阵（或有关参数）的情形；在凸损失函数类和矩阵损失函数下，给出存在一致最小风险无偏估计的充分必要条件．We consider normal growth curve models with covariance matrix, arbitrary orof uniform covariance structure or serial covariance structure. The results of Wu[19], proved inthe context where design matrices have full column ranks and only regression coefficient matrixis estimated, are extended to the situation where design matrices do not need to be of full ranks,and each lineax estimable function of regression coefficient matrix and that of covariance matrix(or related parameters) are simultaneously estimated. The necessary and sufficient conditionsfor the existence of uniformly minimun risk unbiased estimators in problems considered underconvex loss function and matrix loss functions are derived.

关 键 词：增长曲线模型 矩阵损失函数 无偏估计 UMRU 

分 类 号：O212.4[理学—概率论与数理统计]