The Empirical Bayes Statistical Inference Problems Of Parameter For Weibull Distribution Families And Nonexponential Distribution Families Under NA Samples

The empirical Bayes(EB) approach is applicable to statistical inference problems when one is experienced with an dependent sequence of Bayes decision problems each having similar structure,The method has been widely discussed in a great of literature .In this thesis, We mainly study statistical inference of the Empirical Bayes about Weibull distribution and noexponential distribution family parameter under NA samples. Which is introduced in Chapter one. We give the main results of this paper in the Chapter.In Chapter two we investigate the Empirical Bayes (EB) test of scale parameter for Weibull distribution Families in the case of identically distributed and NA samples under linear loss and weighted square loss Functions, By using kernel-type density estimation. The Empirical Bayes test rules are constructed. The asymptotically optional property and convergence rates for the proposed EB test rules are obtained under suitable conditions. Finally an example about the main results of this paper is given.In Chapter three we investigate the Empirical Bayes (EB) estimator of scale parameter for Weibull distribution Families in the case of identically distributed and NA samples under square loss Functions. Under suitable conditions, the proposed EB estimator is asymptotically optional with the convergence rates, Finally an example about the main results of this paper is given.In Chapter four the Empirical Bayes (EB) estimator of parametricθin nonexponential distribution families for NA samples with identically distributed is investigated under square loss Functions, at first, by using kernel-type density estimation. The Empirical Bayes estimation rules are constructed. Under suitable conditions, the proposed EB estimator is asymptotically optional with the convergence rates O ( n? ( rs ? 2)/2( s+ 2)), where s > 2,s∈Nand ( 2 / s < r< 1). Finally an example about the main results of this paper is given.In the fifth Chapter we give a summary and expections.