双边截断型分布族参数函数的渐近最优经验Bayes估计

Asymptotically Optimal Empirical Bayes Estimation for Parameter-functions Of Two-sided Truncation Distribution Families

本文考虑一维双边截断型分布族参数函数在平方损失下的经验 Bayes估计问题 .给定θ,X的条件分布为f (x|θ) =ω(θ1,θ2 ) h(x) I[θ1,θ2 ] (x) dx其中θ =(θ1,θ2 )T(x) =(t1(x) ,t2 (x) ) =(min(x1,… ,xm) ,max(x1,… ,xm) )是充分统计量 ,其边缘密度为 f (t) ,本文通过 f (t)的核估计构造出θ的函数的经验 Bayes估计 ,并证明在一定的条件下是渐近最优的 (a.0 .)

Consider the two\|sided truncation distribution families written in the form f(x｜θ)=ω(θ 1,θ 2) h(x) I \[θ 1,θ 2\] (x), where θ=(θ 1,θ 2) T(x)=(t\-1(x),t\-2(x))=(min(x\-1,…,x\-m),max(x\-1,…,x\-m)) is a sufficient statistic, its marginal density is denoted by f(t).\;In this paper, by estimating f(t), we construct the empirical Bayes estimation (EBE) for parameter\|function Q(θ), and prove the EBE is an asymptotically optimal that of Q(θ).