最好多项母体的渐近最优经验贝叶斯选择规则

An Asymptotic Optimal Empirical Bayes Rule for Selecting Good Multinomial Population in Technology

根据Ｇｉｎｉ—Ｓｈｏｐｓｏｎ指标，在一般的先验分布的情况下，采用离散母体密度函数的加权核估计的方法，研究了最好多项母体的经验贝叶斯选择规则及浙近最优性，并获得了经验贝叶斯风险收敛到贝叶斯风险的收敛速度为Ｏ。

Chinese manufactured goods are frequently divided into several quality grades. Statistical sampling, giving estimated percentage of each grade of product. can potentially aid Chinese engineers to increase percentage of lst grade product, Gini-Simpson index is useful instatiStical sampling. Liang et al in 1990 [1] made use of G-S index under a special condition. We utilize G-S index in a way more generalized than that of Ref. [I]. Now we go intothe mathematics of this paper.The multinomfal distribution provides a model for studying the diversity within a population which is categorized into classes according to a qualitative characteristic. We deal withthe problem of selecting good multinomial population. Let al, ...,π* be k (≥2) m-cell multinomial populationas where πi has the associated cell probability vector pi= (pi1, ..., pim), i=1,2, ...,k. Eq. (6), a general Bayes rule, is obtained for selecting the population associatedwith the largest G-S index. For the situation where prior G belongs to the fsmily F= an aswnptotic optimal empirical Bayes rule is proposed by using the weighted kernel estimation of marginal distribution funchon m (x). Under the restriction of someconditions on the marginal and prior distributions, the rate of convergence of the empiricalBayes risk to the minimum Bayes risk is investigated. The rate of convergence is shown to beO (n-1), where n is the number of independent sets of past data.