| 摘要: |
| 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. |
| 关键词: 非指数分布 密度函数的核估计 经验Bayes估计 收敛速度 NA样本 |
| DOI： |
| 分类号:O212.1 |
| 基金项目:安徽省高校自然科学基金资助项目(KJ2015A345;KJ2013Z252). |
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| EMPIRICAL BAYES ESTIMATOR FOR NONEXPONENTIAL DISTRIBUTION FAMLIIES UNDER NA SAMPLES |
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HUANG Jin-chao
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Basic Course Department, Chouzhou Vocational Technology College, Chuzhou 239000, China
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| Abstract: |
| The empirical Bayes(EB) estimator of parametric θ 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. |
| Key words: nonexponential distribution the kernel estimation of density function empirical Bayes estimation convergence rates NA samples |
