病态加权最小二乘混合模型的k-Liu估计解法  

k-Liu Estimation Method for Morbid Weighted Least Squares Mixed Model

作　　者：陈丽 王岩[1] 邵德盛[1,2] Chen Li;Wang Yan;Shao Desheng(Information Center,Yunnan Earthquake Agency,Kunming 650201,China;College of Land Resource Engineering,Kunming University of Science and Technology,Kunming 650093,China)

机构地区：[1]云南省地震局信息中心,昆明650201 [2]昆明理工大学国土资源与工程学院,昆明650093

出　　处：《统计与决策》2024年第8期17-21,共5页Statistics & Decision

基　　金：国家重点研发计划课题(2018YFC1503604)。

摘　　要：文章综合加权多源观测模型及最小二乘混合模型,组合两种有偏估计算法得到组合有偏估计算法。利用岭估计与Liu估计形成一种新的有偏估计——k-Liu估计,其可以抵抗法方程系数矩阵的病态性,同时可以有效降低参数估值的均方误差。通过构建目标函数导出k-Liu估计在病态最小二乘混合模型中参数的通用解式、均方误差式和协因数的计算式,推导出k-Liu估计中修正因子的计算式,通过广义交叉检核法确定岭参数。最后,通过多种估计法参与算例解算,得出k-Liu估计可以进一步提升混合最小二乘模型的解算精度。This paper synthesizes weighted multi-source observation model and least square mixed model,and combines two biased estimation algorithms to get a combined biased estimation algorithm.A new biased estimation—k-Liu estimation is formed by using ridge estimation and Liu estimation,which can effectively reduce the mean square error of parameter estimation while re-sisting the morbid coefficient matrix of normal equation.By constructing the objective function,the general solution formula,mean square error formula and cofactor calculation formula of the parameters of the k-Liu estimation in the morbid least squares mixed model are derived;the calculation formula of the correction factor in the k-Liu estimation is derived,and the ridge parameters are determined by the generalized cross-validation method.Finally,a variety of estimation methods are used for the calculation of ex-amples to draw the conclusion that the k-Liu estimation can further improve the calculation accuracy of the mixed least squares model.

关 键 词：病态性 最小二乘混合模型 岭估计 k-Liu估计 广义交叉检核法 

分 类 号：O212.1[理学—概率论与数理统计] P207.2[理学—数学]