The Empirical Bayes Estimation Of Parameter For Scale-exponential Family And The One-side Truncated Distribution Family Under Associated Samples

The empirical Bayes(EB) approach is applicable to statistical inference problems when one is experienced with an sequence of Bayes decision problems each having similar structure. The method has been widely discussed in a great of literature which is introduced in Chapter one. Also we give the main results of this paper in this Chapter.In the second and third chapter, The Bayes estimator of the parameter is obtained for the scale exponential family in the case of positively associated (PA) and weakly stationary sample with identically distributation under weighted square loss function. We prove that the estimator is not only an asymptotically optimal E·B estimator but also the convergence rate of the proposed E·B estimator is also obtained. Finally, two examples have been given that satisfies the conditions of the main results.In the fourth chapter, we construct the E·B estimator for parameter function of one-side truncated distribution under identically distribution, positively associated (PA) and weakly stationary data. Also, we obtained its convergence rate.In the fifth chapter, under identically distributed, positively associated (PA) and weakly stationary samples, the Bayes estimator is also derived under Linex loss function and empirical Bayes (E·B) estimator of parameter are constructed for the one-side truncated families. It is shown that the proposed EB estimator is asymptotically optimality and we also obtain its convergence rate. At last, we give an example that satisfies the conditions of theorem.Finally, in the sixth chapter, we make a summary and give expections.