Strong Consistency of Approximate Maximum Likelihood Estimators with Applications in Nonparametrics
Strong Consistency of Approximate Maximum Likelihood Estimators with Applications in Nonparametrics
复制标题
近似最大似然估计与非参数应用的强一致性
DOI：
10.1214/aos/1176349647
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发表时间：
1985
期刊：
影响因子：
--
通讯作者：
Jane
中科院分区：
文献类型：
--
作者：
Jane
Wald的一般分析条件，暗示强一致性的近似最大似然估计（AMLE）已延长勒卡姆，基弗和沃尔福威茨，胡贝尔，Bahadur，和帕尔曼。所有这些条件都使用log[f（x，0）/f（x，60）]类型的对数似然比，其中Oo是参数的真值。然而，这些方法通常在非参数情况下失败。因此，在本文中，对于每个0 $00，我们查看log[f（x，0）/f（x，r（0））]类型的对数似然比，其中Oi（0）是在60的邻域Vi中选择的某个参数。给出了AMLE强相合的一般解析条件。结果表明，适用于几个非参数的家庭密度，例如，凹分布函数和增加的失效率分布。特别是，它们可以应用于几个删失数据的情况下。
Wald's general analytic conditions that imply strong consistency of the approximate maximum likelihood estimators (AMLEs) have been extended by Le Cam, Kiefer and Wolfowitz, Huber, Bahadur, and Perlman. All these conditions use the log likelihood ratio of the type log[f(x, 0)/f(x, 60)], where Oo is the true value of the parameter. However these methods usually fail in the nonparametric case. Thus, in this paper, for each 0 $ 00, we look at the log likelihood ratio of the type log[f (x, 0)/f (x, r(0) )], where O,(0) is a certain parameter selected in a neighborhood V, of 60. Some general analytic conditions that imply strong consistency of the AMLE are given. The results are shown to be applicable to several nonparametric families having densities, e.g., concave distributions functions, and increasing failure rate distributions. In particular, they can be applied to several censored data cases.