自Robbins于 1955年提出经验 Bayes 方法以来，经验Bayes 方法的研究一直是统计研究的一个重要领域，取得了一系列重要研究成果，这些研究大多集中在独立样本情形，然而，在经济、医药和可靠性等领域，随机变量常常不是独立的， 而是有一定的相关性，α混合随机变量就是常见的情形之一，是条件最宽的一类混合序列，有广泛的应用背景，因此α混合样本下的经验 Bayes统计推断是理论和实际应用中的一个重要的研究课题。 本项目拟系统研究α混合样本下几类重要分布族，如单参数指数分布族、刻度指数族、单边或双边截断分布族等分布族参数的经验Bayes 估计和检验，在上述研究的基础上，研究其它相依样本情形经验 Bayes 估计和检验问题，争取较系统地建立相依数据结构下经验Bayes 统计推断的理论。

Since Robbins proposed the empirical Bayes method in 1955, the study of empirical Bayes method has been one of the important statistical research fields. A lot of significant results have appeared in the study of the method, which are mainly related to the case of independent samples. However, many samples are usually not independent in the fields of economy, medicine and reliability, which are usually dependent. A sample of α-mixing random variables is one of the commonly occurred dependent structures, which is the weakest mixing random variable sequence and has very broad application background. Therefore, statistical inference based on empiricalBayes method is an important research topic theoretically and practically under α-mixing samples.This project will systematically investigates the empirical Bayes estimation and test for the parameters of some important distribution families such as singleparametric exponential family, scale exponential family and one-tail or two-tail truncated family under α-mixing samples. Based on above experience, we will also study the empirical Bayes estimation and test under other dependent samples.Our goal is to systematically build up a statistical inference theory based on the empirical Bayes method under dependent samples.