The Empirical Bayes Test Of A Class Of Location And Scale Parameters

This paper focuses on the two-sided empirical Bayes(EB) test of parameter for the scale exponential family under weighed loss function and the empirical Bayes(EB) test of location parameter for a kind of Gamma distribution.In the first chapter, the principle of Bayesian methods, the empirical Bayesian methods, the current research states and recent development of them are retro-spected and introduced. The structure and main content of the thesis are also briefly introduced.In the second chapter, the two-sided empirical Bayes(EB) test of parameter for the scale exponential family under weighed loss function is discussed. The EB test rules are constructed by kernel estimation method.The asymptotically optimality and convergence rates of the EB test rules are obtained. Finally, an example satisfying the conditions of the theorems are shown.In the third chapter, the Bayes and empirical Bayes(EB) test of location parameter for a kind of Gamma distribution is discussed. The EB test rules are constructed by the empirical distribution function and kernel estimation of probability density function and its derivatives. The asymptotically optimality of the EB test rules are obtained.