多因变量多元线性模型主成分型预测的最优性判别  

Superiority discrimination of principal component prediction in the multivariate linear model with multiple dependent variables

作　　者：黄云腾[1] 朱宁[1] 廖苑蓉[1] 张立强[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2013年第5期412-415,共4页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(71001015)

摘　　要：针对多因变量多元线性模型有偏预测问题,结合主成分估计,构造主成分型预测量。通过主成分型预测与最优线性无偏预测的最优性判别问题进行分析,分别得到了主成分型预测在R(i)(·)准则、MDE-准则及RT(·)下优于最优线性无偏预测的充分条件。结果表明,在一定条件下,有偏的主成分型预测优于最优线性无偏预测。Based on the theory of principal component estimate, a principal component prediction is structured to solve the biased prediction problem of the multivariate linear model with multiple dependent variables. The superiority dis- crimination between the principal component prediction and the best linear unbiased prediction in the multivariate linear model is analyzed. The sufficient conditions about the superiority of the principal component prediction under the rule R（i） （ ＊ ）, MDE and RT （ ＊ ） compared with the best linear unbiased prediction are given. The result proves that a principal component prediction is superior to the best linear unbiased prediction under some conditions.

关 键 词：多因变量多元线性模型 最优线性无偏预测 主成分型预测 

分 类 号：O212.4[理学—概率论与数理统计]