抗差岭型主相关估计及其误差影响

Robust Ridge and Principal Correlation Estimation and Influence of Error

针对法方程系数阵病态和观测值存在粗差对估值结果造成双重影响的问题,在岭型主相关估计的基础上引入抗差M估计模型,提出了一种抗差有偏估计的新方法——抗差岭型主相关估计。推导出了相应模型的抗差解及误差影响函数,并进行了计算分析。与主成分估计不同的是,该方法按主成分对观测值的影响程度大小对其进行舍取,在尽可能保留有用观测信息的基础上克服了病态性和粗差的影响。

In order to solve the problem of both ill-conditioned and outlier, a robust ridge and principal correlation estimation was established based on the M-model of the robust estimation theory. By using a numerical example, some calculation and comparison were performed. The result showed that this new approach could not only improve the illconditioned equations, but also resist the effect of course errors effectively. Different from the principal components estimation, this method choosed the principal components according to its correlation with the observations. And this reserved more useful information.