| In this paper,we mainly investigate the Bayes prediction of linear and quadratic quantities in a finite normal population.We also discuss the parametric empirical Bayes prediction of population total under the finite normal population.In the first chapter,we introduce the finite population model and the research progress on prediction problem in finite population model,the principle of Bayesian methods and empirical Bayesian methods.The significance and structure of this paper are also introduced.In the second chapter,we mainly investigate the Bayes prediction of linear and quadratic quantities in a finite population.Firstly,we give the Bayes prediction of population quantities by the normal inverse-Gamma prior and non-information prior,respectively.Secondly,we further obtain the Bayes prediction of linear and quadratic quantities and their Bayes prediction risk.Finally,we give some examples to illustrate the theoretical results.In the third chapter,we mainly investigate the parametric empirical Bayes prediction of population total under the finite normal population.First of all,we obtain the Bayes prediction of population total based on the ideal of Bayesian analysis.Besides,the parametric empirical Bayes prediction(PEBP)of population total is constructed by using of historical samples since the Bayes prediction is not used in practice.Finally,the superiority of PEBP over BLUP of the population total is discussed under the mean square error(MSE)criterion. |
