Optimal and minimax prediction in multivariate normal populations under a balanced loss function

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• 作者：Guikai Hu^a ; ^b ; ^{huguikai97@163.com" class="auth_mail} ; Qingguo Li^a ; ^{liqingguoli@yahoo.com.cn" class="auth_mail} ; Shenghua Yu^c ; ^{yshh1966@163.com" class="auth_mail}
• 关键词：62M20 ; 62C15
• 刊名：Journal of Multivariate Analysis
• 出版年：July 2014
• 年：2014
• 卷：128
• 期：Complete
• 页码：154-164
• 全文大小：413 K

文摘

Under a balanced loss function, we investigate the optimal and minimax prediction of finite population regression coefficient in a general linear regression superpopulation model with normal errors. The best unbiased prediction (BUP) is obtained in the class of all unbiased predictors. The minimax predictor (MP) is also obtained in the class of all predictors. We prove that MP is unique in the class of all predictors and is better than BUP in a certain region of parameter space. Next, we give some conditions for optimality of the simple projection predictor (SPP) and prove that MP dominates SPP on certain occasions.