Minimax And Empirical Bayes Prediction Research In A Finite Population

This paper mainly studies the prediction of linear predictable variable in finite population with ellipsoid constraint and empirical Bayesian predictionT_EBP of population total T in finite population with normal inverse gamma prior information.The main research contents are as follows:Firstly we introduce the research progress of finite population forecasting method minimax decision-making method empirical Bayes method and the significance and structure of this paperSecondly we study the prediction problem of linear predictable variable in finite population with ellipsoid constraint and matrix loss function.We obtain the linear minimax prediction in the homogeneous prediction class.Then we give some examples to illustrate the existence.Thirdly we study the empirical Bayesian prediction problem in finite population with normal inverse gamma prior information.The Bayesian prediction of T is obtained by the new method and then empirical Bayesian predictionT_EBP is obtained by the EB method.Finally we verify thatT_{EB P}is asymptotically optimal and T_EBP is better than the best linear unbiased predictionT_BLUP by numerical simulation under the mean square error（PMSE）criterion.Finally based on summarizing the work of this article and looking forward to the work to be studied in the future.