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.
作者
陈丽
王岩
邵德盛
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)
出处
《统计与决策》
CSSCI
北大核心
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)。
