套重复测量模型的充分性和估计

摘要

当每一个体有相同的子个体,并且每一子个体的处理水平是成对的时候,我们使用套重复测量模型.令Yi=(Yilll,…Yimrc)′是第i个个体的观测向量.假设Yi为相互独立的正态分布,均值为μi,协方差阵为∑＞0.假设可简化为所有测量值的方差为σ2;相同个体的不同子个体之间的成对测量值之间的关系如下:(1)不同列不同行的观测值;(2)相同列不同行的测量值;(3)相同行不同列的测量值,它们的协方差分别为ρ2σ2,ρ3σ2,ρ4σ2.我们假设试验是给定的,用坐标自由(coordinate-free)的方法研究了套重复测量模型的完备充分统计量,最小方差无偏估计(MVUE)和极大似然估计(MLE).%A nested repeated measures model occurs in analysis of variance when a particular individual has the same number of subindividuals and each subindividual receives every pair of treatment levels. Let Yi =pendently normally distributed with meanμi and common covariance ∑＞ 0. The simplifying assumptions that all measurements have the same variance σ2, every pair of measurements that comes from different subindividuals but the same individual has covariance σ2ρ1; and every pair of measurements that comes from the same individual and same subindividual with (i) different columns and different rows treatments, (ii) the same column but different rows treatments, (iii) different columns but the same.row treatments have σ2ρ2, σ2ρ3, σ2ρ4 as their respective covariances is. made. We assume that the design is given and use a coordinate-free approach to derive a complete sufficient statistic, minimum variance unbiased estimators (MVUE) and maximum likelihood estimators (MLE) for the nested repeated measures model.