均方误差准则下的几乎无偏Stein岭型主成分估计的优良性  

The Optimal Property of Almost Unbiased Stein Ridge Type Principal Component Estimator Under Mean Square Error

作　　者：朱宁[1] 刘庆华[1] 周桂兰[1] 农以宁[2] 

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 [2]桂林电子科技大学生命与环境科学学院,广西桂林541004

出　　处：《河南师范大学学报（自然科学版）》2017年第5期1-6,共6页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家科技支撑计划课题(2015BAL04B0305);广西科技重点研发计划项目(桂科AB16380321);广西自然科学基金项目(2016GXNSFBA380102);桂林电子科技大学研究生教育创新计划(2016YJCX48)

摘　　要：将Stein岭型主成分估计利用几乎无偏估计思想进行优化,得到几乎无偏Stein岭型主成分估计.并考虑均方误差准则,得到了几乎无偏Stein岭型主成分估计优于最小二乘估计、Stein岭型主成分估计的充分条件.并通过数值实验证明在给定k或p时,几乎无偏Stein岭型主成分估计的均方误差与Stein岭型主成分估计的均方误差较为接近,且远大于最小二乘估计的均方误差.We optimize the Stein ridge type principal component estimator by using the mind of almost unbiased estimator,and we get the almost unbiased Stein ridge type principal component estimator.In terms of the mean square error criterion,some sufficient conditions for the almost unbiased stein principal component estimator being better than the least squares estimator,the almost unbiased stein principal component estimator being better than the stein principal component estimator are given.Through numerical experiments,when kor pis given,it proves that the mean square error of the almost unbiased Stein ridge type principal component estimator is relatively close the Stein ridge type principal component estimator,and it is greater than the least squares estimator.

关 键 词：均方误差 几乎无偏估计 岭型主成分估计 优良性 

分 类 号：O212.1[理学—概率论与数理统计]