The Empirical Bayes Estimation And Test Of Parameter For Scale-Exponential Family UnderAssociated Samples

We know the scale-exponential family is a wide range of distribution, such as the exponential distribution, Weibull distribution, gamma distribution are closely related; it is widely used reliability in industrial, actuarial and survival analysis.Since the empirical Bayesian (EB) method is introduced, there have been many literatures to discuss the scale-exponential family parameter empirical Bayesian estimation and test problems, the research literature in the vast majority are often independent and identically distributed samples, however the permeability theory and reliability theory and practical problems, the obtained samples are often not independent, but has some relevance, such as positive associated (PA) and negative associated (NA) random samples are two common associated samples, so the research about the empirical Bayesian estimator and test of parameter for scale-exponential family under associated samples has theoretical value and practical significance.In the first chapter, the principle of Bayesian methods, the EB methods, the current research states and development of them in the scale-exponential family are retrospect and introduced. The structure and main content of thesis are also briefly introduced.In the second chapter, this article is based on previous research, In this paper, asymptotically optimal empirical Bayesian estimator of parameter is studied for scale-exponential family under PA samples, the Bayesian estimator of parameter is derived under the scale squared error loss function. By the method of kernel estimation, the empirical Bayesian estimator of the parameter is then constructed, and the asymptotic optimality of the estimator is proved. Finally, an example is presented.In the third chapter, this article is based on the weighted product loss function the study about the two-sided empirical Bayesian test of parameter for scale-exponential family was discussed under PA samples. By using the method of kernel estimation for its probability density function and its derivative function, the empirical Bayesian test was constructed and the asymptotic optimality and convergence rates of the empirical Bayesian test rules was proved. Finally, an example was given.