Of Na Sample Case Study Of Empirical Bayes Statistical Inference And Its Applications

This dissertation is to apply Bayesian and empirical Bayesian theory to investigate the statistical inference of parameters in one-side, two-side truncated family and one-parameter exponential family and some reliability problem.Firstly, in the case of NA samples the asymptotically optimal empirical Bayes (EB) estimation and EB test for one-side truncation parameters are studied by using density kernel estimator and under some certain conditions convergence ratesO(n ) are obtained that can arbitrarily approach to the best rates O(n-1).Secondly, under asymmetric linex loss function the EB decision function of two-side truncation parameter is constructed and proved to be asymptotically optimal with convergence rates. Combining NA samples the EB estimation with convergence rates is also obtained;Thirdly, for one-parameter exponential distribution family, we give the parameters' EB estimator that is admissible and asymptotically optimal with convergence rates.Finally, Bayesian and hierarchical Bayesian approaches are applied to analyze the reliability performances for series system with cold standby units and the numerical simulation results show that multiple Bayes estimator is superior to Bayes estimator.