NA样本下非指数分布族参数的经验Bayes估计

EMPIRICAL BAYES ESTIMATOR FOR NONEXPONENTIAL DISTRIBUTION FAMLIIES UNDER NA SAMPLES

在"平方损失"下,研究了基于NA样本情形下非指数分布族参数θ的经验Bayes估计.利用概率密度函数的核估计,构造了参数的经验Bayes(EB)估计量,在适当的条件下证明了获得的(EB)估计是渐近最优的且收敛速度的阶为O(n^(-(rs-2)/2(s+2))),其中s>2,s∈N,2/s<r<1.最后给出一个满足定理条件的例子.

The empirical Bayes（EB） estimator of parametric 6 in nonexponential distribution families for NA samples is investigated under square loss functions.By using kernel-type density estimation,the empirical Bayes estimation rules are constructed.Under suitable conditions,it is shown that the proposed EB estimators are asymptotically optimal with convergence rates O（n^-（rs-2）/2（s＋2））,where s〉2,s∈N,2/s〈r〈1.Finally an example about the main results of this paper is given.