一种新的岭估计解法及精度评定  

A New Ridge Estimation Method and Precision Evaluation

作　　者：翁烨 邵德盛[1,2] Weng Ye;Shao Desheng(Seismological Bureau of Yunnan Province,Kunming 650200,China;Faculty of Land Resource Engineering of KUST,Kunming 650093,China)

机构地区：[1]云南省地震局,云南昆明650200 [2]昆明理工大学国土资源与工程学院,云南昆明650093

出　　处：《城市勘测》2022年第1期69-73,79,共6页Urban Geotechnical Investigation & Surveying

基　　金：李建成院士工作站(2015IC015);国家重点研发计划课题“中国大陆主要活动构造断裂带的分段运动特征研究”课题编号是(2018YFC1503604)。

摘　　要：在多元线性回归模型中,经典最小二乘解称为最优线性无偏估计解,系数矩阵的复共线性导致最小二乘参数解变得极不稳定。针对测量系统中的病态问题求解,结合岭估计和主成分估计的优势,推导出一种新的岭估计解法,验证了该方法的可行性。利用均方误差极小化,得出不同岭参数的求解公式及新估计的精度评定方法。通过算例证明了在均方误差有意义下,新的岭估计解法优于最小二乘估计和狭义岭估计解法。In the multivariate linear regression model,the classical least squares solution is called the optimal linear unbiased estimation solution,and the complex collinearity of the coefficient matrix makes the least squares parameter solution extremely unstable.In view of the ill-conditioned problem solving in the measurement system,a new ridge estimation method is derived by combining the advantages of ridge estimation and principal component estimation,and the feasibility of this method is verified.Using the mean square error minimization,the solution formulas of different ridge parameters and the accuracy evaluation method of the new estimation are obtained.Numerical examples show that the new ridge estimation method is superior to the least squares estimation and the narrow ridge estimation method in the sense of mean square error.

关 键 词：多元线性回归 最小二乘 主成分估计 岭估计 均方误差 

分 类 号：P207[天文地球—测绘科学与技术]