多参数离散指数族参数渐近最优的经验Bayes估计的收敛速度

The convergence rates of empirical Bayes estimation for the parameters of multi-parameter discrete exponential family

摘要: 本文构造了多参数离散指数族参数的渐近最优的经验Bayes（EB）估计,若记R_n(δ_n,G)为δ_n的全面Bayes风险,R_G最小Bayes风险,则在某些条件下,c_1 n^-1λ＜1,μ＞2成立，其中c₁, c₂为正的常数。

Abstract: Asymptotically optimal empirical Bayes （EB） estimators δ_n for the parameters of multi-parameter discrete exponential families are proposed. Under suitable conditions, we prove that, the overall Bayes risk of EB estimatorsconverge to the minimum Bayes risk with ratec_1 n^-1λ＜1 and μ＞2, for some positive constants c₁, c₂.