Empirical Bayesball Remixed: Empirical Bayes Methods for Longitudinal Data
Empirical Bayesball Remixed: Empirical Bayes Methods for Longitudinal Data
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DOI：
10.1002/jae.2530
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发表时间：
2017-04-01
影响因子：
2.1
通讯作者：
Koenker, Roger
中科院分区：
文献类型：
--
作者：
Gu, Jiaying;Koenker, Roger
考虑了涉及纵向数据的高斯和二项式复合决策问题的经验贝叶斯方法。最近的凸优化重构的非参数最大似然估计的基弗和沃尔福威茨（数学统计年鉴1956年; 27：887-906）被用来构建非参数贝叶斯规则的复合决策。该方法与应用程序来预测棒球击球平均数，和击球性能的年龄分布。经验应用的一个重要方面是一般的双变量规格的分布异构的位置和规模效应的球员表现出弱的正相关的位置和规模属性。使用所提出的方法，根据前十年的表现预测2012年球员的击球率，结果显示，与对未观察到的异质性进行更严格的处理的更幼稚的方法相比，性能得到了大幅改善。比较也与非参数贝叶斯方法的基础上Dirichlet过程先验，它可以被看作是一个正规化，或平滑，版本的Kiefer-Wolfowitz方法。版权所有（c）2016约翰威利父子有限公司
Empirical Bayes methods for Gaussian and binomial compound decision problems involving longitudinal data are considered. A recent convex optimization reformulation of the nonparametric maximum likelihood estimator of Kiefer and Wolfowitz (Annals of Mathematical Statistics 1956; 27: 887-906) is employed to construct nonparametric Bayes rules for compound decisions. The methods are illustrated with an application to predict baseball batting averages, and the age profile of batting performance. An important aspect of the empirical application is the general bivariate specification of the distribution of heterogeneous location and scale effects for players that exhibits a weak positive association between location and scale attributes. Prediction of players' batting averages for 2012 based on performance in the prior decade using the proposed methods shows substantially improved performance over more naive methods with more restrictive treatment of unobserved heterogeneity. Comparisons are also made with nonparametric Bayesian methods based on Dirichlet process priors, which can be viewed as a regularized, or smoothed, version of the Kiefer-Wolfowitz method. Copyright (c) 2016 John Wiley & Sons, Ltd.