利用复共线性诊断确定偏差矫正项的截断型岭估计  

Truncation Ridge Estimation Based on the Biased-corrected Theory by Multicollinearity Diagnosis

作　　者：郭杰[1] 归庆明[1] 郭淑妹[1] 张宁[1] 

机构地区：[1]信息工程大学理学院,河南郑州450001

出　　处：《武汉大学学报（信息科学版）》2015年第6期785-789,794,共6页Geomatics and Information Science of Wuhan University

基　　金：国家自然科学基金资助项目(41174005;40974009);中国卫星导航学术年会青年优秀论文获奖者资助项目~~

摘　　要：为了避免有偏估计的偏差对可靠部分的影响,提出了偏差矫正的正则化方法,但是偏差矫正项的选取是个关键问题。首先采用复共线性诊断、度量和检验所获得的重要信息,对受复共线性危害严重的分量进行估计,且使得均方误差达到极小。然后基于偏差矫正的正则化解法的一般理论,得到偏差矫正的分析性条件,从而得到一种新的基于复共线性诊断确定偏差矫正项的截断型岭估计。最后通过算例分析验证了该方法在提高解的质量、参数估值的准确性和稳定性方面的优良性。In order to avoid the bad effect provided by the biases of the biased estimation, bias-corrected regularization is presented. But how to choose the bias-corrected term is a key link. In this paper, based on the key information from the multicollinearity diagnosis, measurement and test, parameters seriously harmed by the multicollinearity are estimated. Then based on the bias-corrected theory ,the analytical condition of the bias-corrected regularization is derived. Truncation ridge estimation based on the bias-corrected theory by multicol Iinearity diagnosis is proposed. The numerical results demonstrate that the new method can improve the numerical stability and accuracy of parameter estimation.

关 键 词：病态性 复共线性 信噪比 均方误差 偏差矫正正则化 

分 类 号：P207.2[天文地球—测绘科学与技术]