摘要
考虑一般的线性模型Y=Xβ+ε,其中X为n×p阶设计矩阵,β为p×1未知参数向量,e为n×1随机误差向量。满足E(ε)=0,Cov(ε)=σ~2∑,这里σ~2>0可能未知,Σ则为已知的非负定矩阵,θ是β的一个线性函数,且可估,假设θ_R为Rao型最小二乘估计,本文证明了若随机误差服从ε椭球等高分布,则θ_R满足所谓最大概率性质,即θ_R落在以θ为中心的任一椭球内的概率不小于θ的任一性线无偏估计落在同一椭球内的概率,推广了文献中的结果。
Consider the linear model Y-Xβ+ε,where Y is the response variable of order(n×1),X is an(n×p)matrix of known constants,β is a (p×1) unknown parameter,ε is an(n×1)error variable with E(ε)=0 and E(εε')=Cov(ε)=σ~2∑,where ∑≥0 is known and σ~2>0,possibly unknown. Suppose that θ is a Jinear components of β.In this paper we show that if e is assumed to have a distribution belonging to the class of elliptical distributions,the probability of the Least Square estimator of θ falling inside any fixed ellipsoid centered at θ is greater than or equal to the probability that any linear unbiased estimator of θ falls inside the same ellipsoid,extending the result of Ali and Ponnapalli[1]
出处
《安徽大学学报（自然科学版）》
CAS
1991年第3期10-14,共5页
Journal of Anhui University(Natural Science Edition)
基金
国家青年科学基金18901001资助的课题
关键词
线性模型
最小二乘估计
最优性质
least square estimator
elliptical distribution
maximum probability estimator
linear model
