摘要
对于正态分布族{N(μ,σ~2)|-∞<μ<+∞,σ~2>0},本文利用Robbins,Tao Bo 的思想,分别构造了μ,σ~2,θ=(μ,σ~2)′的线性经验 Bayes估计,我们不但在一定条件下讨论了这些估计的 a.o 收敛速度,而且证明了其 a.s 收敛性.
In the paper the family of normal distribution{N(μ,σ~2)| -∞<μ<+∞,σ~2>0} is considered.The linear empirical Bayes estimators of μ,σ~2 and θ=(μ,σ~2)′ are constructed by the method of Robbins and Tao Bo.On some conditions asymptotically optimal convergence and almost sure convergence of these estimators are obtained.
关键词
参数向量
BAYES
正态分布族
parameter vector
linear empirical Bayes estimation
asymptotically optimal convergence
almost sure convergence
