相依情形下的经验Bayes统计分析及应用研究

【作者】 严拴航；

【导师】 师义民；

【作者基本信息】 西北工业大学 ， 统计学， 2007， 硕士

【摘要】 本文在样本相依情形下，将Bayes、经验Bayes理论应用于正指数族参数、刻度指数族参数及单参数总体参数的统计分析研究，并对相依部件串、并联系统的可靠性指标进行了Bayes分析。主要内容包括以下几个方面： 1．运用同分布PA样本密度函数的核估计，构造了一类正指数分布族参数的经验Bayes检验，讨论了它的渐近最优性，并建立其收敛速度。在适当的条件下，证明了该收敛速度可以任意接近O(n^-1)。 2．在非对称Linex损失函数下，讨论了一类刻度指数族参数的经验Bayes估计（PA样本情形）问题，证明了EB估计的渐近最优性，并给出了收敛速度的阶。 3．在m相依样本情形下，用经验Bayes方法对单参数总体中的未知参数进行研究，得到其相应的线性经验Bayes估计，并给出了渐近最优的收敛速度O(N^-1/4C_N^-1)。 4．对具有不同失效率的n个相依部件组成的串、并联系统进行研究，在建立相应失效模型的同时，给出系统分布参数、可靠度及失效率等可靠性指标的Bayes估计。更多还原

【Abstract】 In this paper, Bayesian theory and empirical Bayesian theory are used to study the parameter estimation of the distribution families. Using empirical Bayes methods , the parameters for positive exponential family and scale exponential family are discussed in the case of PA samples. Moreover, one-parameter distribution family parameter is discussed as the samples are m dependent. In the end, the reliability performances for series and parallel systems with n dependent components are studied.1. By using the kernel-type density estimation in the case of identically distributed and positively associated （PA） samples, the empirical Bayes （EB） test rules for the parameter of a positively exponential family are constructed and the asymptotic optimality is obtained. It is shown that the convergence rates of the proposed EB test rules can arbitrarily close to O(n^-（?）) under certain condition.2. For the scale-exponential family, the empirical Bayes estimation of the parameter are exhibited under asymmetric linex loss function. Combining PA samples, the EB estimators are discussed and the rates of convergence are also obtained.3. Based on m dependent samples, the linear EB estimation of the parameter is discussed . also the asymptotically optimal rates of convergence O(N^{-（?）/（?）}C_N^-（?）) is obtained.4. For the reliability parameters in n non-independent series and parallel systems with dependent time failure rates, the corresponding failure models are constructed. Meanwhile, we give the Bayesian estimation of reliability performances such as system parameters, reliability and failure rates.更多还原