The Empirical Bayes Estimation In A Number Of Issues

Empirical Bayesian theory is applied to investigate the statistical inference problems of the parameter of one-side truncated families, the parameter of two-dimensional two-side truncated distribution families, location parameter in double parameters exponential distribution under the identically distribution and negatively associated samples, linex loss function and quadratic loss in this dissertation.Firstly, in the case of NA samples, the problems of the parameter of one-side truncated families is studied using the linex loss function. the EB estimator for the parameter is constructed by the method of kernel density .The convergence rates can be obtained.Secondly, for location parameter in double parameters exponential distribution, the empirical Bayes estimator of the parameter is studied under the quadratic loss function and NA samples, and the rates of convergence is also obtained.Finally, for the parameter of two-dimensional two-side truncated distribution families, the empirical Bayes estimator of the parameter is disscused .