摘要
本文研究了线性模型中参数的经验Bayes检验的渐近最优性及其收敛速度问题。假设模型为Y=Xβ+ε,基中ε～N(0,σ~2I),σ~2未知。通过利用X,Y和n个相互独立的历史样本,我们构造了θ=(β~1,σ~2)′的经验Bayes检验,并证明了该检验与最优的Bayes检验相比是渐近最优的,而且其收敛速度可以任意接近O(n^(-1/2))。
The purpose of this paper is to investigate the asymptotical optimality and the convergence rates of a sequence of empirical Bayes decision rules for two-action decision problems where the observations belong to the following model Y=Xβ+ε, where ε～N(0,σ~2I),σ~2 is unknown. Using X,Y and the information contained in the observation vectors obtained from n independent past samples of the problem, the empirical Bayes testing procedures for θ=(β′, σ~2)^(?) are exihibited. The testing procedures are compared with the optimal Bayes testing procedure and are shown to be asymptotically optimal with rate near O(n^(-1/2)).
关键词
线性模型
线性回归
贝叶斯检验
empirical Bayes, multiple linear regression model, asymptotical optimality, convergence rate
