一类离散分布参数的经验Bayes估计的收敛速度

Empirical Bayes Estimation with Convergence Rates about a Class of Discrete Distribution Families

中文摘要:

      

英文摘要:

      In this paper we consider a family of discrete distributions f_θ(x)dμ(x), and suppose that the Bayes estimate of φ(θ) with respect to the priori distribution H∈H has a form dH(x) =(?)a_k(x)f(x k)/f(x). where f(x)=∫f_θdH(θ) . we construct asequence of empirical Bayes estimates and establish its rate of convergence, and prove that under suitable conditions this rate of convergence can arbitrarily close to 1. we also give a counter-example to the main Theorem 2.1 of [5], and then declare that the "Theorem" does not hold.