Several Types Of Parameters Using Empirical Bayes Statistical Analysis: The Pa Sample Situation

Bayesian and empirical Bayesian theory is applied to investigate the statistical inference problems of the parameters for scale-exponential, continuous one-parameter exponential and one-side truncated families under the identically distributed and positively associated (PA) samples in this dissertation.Firstly, in the case of PA samples, the empirical Bayes (EB) test problem about scale-exponential family is studied using weighted linear loss function. A sequence of EB test functions for the parameter are constructed by the method of kernel density function estimation and their asymptotic optimal property are gotten; under some suitable conditions, the convergence rates can be terrified arbitrarily approaching tothe best convergence rates O(n~-1).Secondly, for the continuous one-parameter exponential family, the empirical Bayes estimators of the parameter are exhibited under quadratic loss function. Combing PA samples, the EB estimators are discussed and the rates of convergence are also obtained.Finally, under PA samples, the empirical Bayes estimators of the location parameter in one-side truncated family are given with certain convergence rates.