平衡损失下有限总体回归系数的最优预测  

Optimal Predictor of Finite Population Regression Coefficient under a Balanced Loss Function

作　　者：胡桂开[1] 吴志强[1] 

机构地区：[1]东华理工大学理学院,江西南昌330013

出　　处：《东华理工大学学报（自然科学版）》2015年第3期331-334,共4页Journal of East China University of Technology(Natural Science)

基　　金：国家社会科学基金(12BTJ014);江西省自然科学基金(20122BAB211007;20144BAB2110001)

摘　　要：在平衡损失下,研究超总体中有限总体回归系数的最优预测。在Gauss-Markov型误差假定下,得到了齐次线性预测,为有限总体回归系数最优线性无偏预测的充分必要条件,并在几乎处处意义下得到了唯一的最优线性无偏预测。结果表明,平衡损失下的最优预测是误差平方和下的最优预测和预测均方误差准则下最优预测的平衡。同时,证明了最优线性无偏预测在齐次线性预测类中的可容许性。Under a balanced loss function,the optimal predictor of finite population regression coefficient in superpopulation model are investigated. Necessary and sufficient conditions for homogeneous linear predictors to be a best linear unbiased predictor( BLUP) under the Gauss-Markov assumption are obtained. The unique best linear unbiased predictor is obtained in the sense of almost surely. The results show that BLUP under the balanced loss function is a balance between the BLUP under residual sum of squares and the BLUP under prediction mean squared error. Next,it prove that the BLUP is admissible in the class of homogeneous linear predictors.

关 键 词：最优预测 有限总体回归系数 平衡损失 

分 类 号：O212.1[理学—概率论与数理统计]