线性模型参数的稳健化有偏估计

本文讨论复共线性和粗差同时存在时线性模型的参数估计问题，基于等价权原理提出了一个稳健有偏估计类（稳健压缩估计），并且建立了稳健压缩估计的计算方法，为了满足实际问题的需要，构造了许多很有意义的稳健有偏估计，例如稳健岭估计、稳健主成分估计，稳健组合主成估计、稳健单参数主成分估计、稳健根方估计等等，最后通过一个算例表明，本文提出的稳健有偏估计具有既可克服复共线性影响又可抵抗粗差干扰的良好性质。

Robustifying Biased Estimation in Linear Model

The parameter estimation problem in linear model is considered when multicollinearity and outliers exist simultaneously.A class of new estimators,robust general shrunken estimators,are proposed by grafting the robust estimation techniques philosophy into the biased estimator,and their statistical properties are discussed.By appropriate choices of the shrinking parameter matrix,we obtain many useful and important estimators.A numerical example is used to illustrate that these new estimators can not only effectively overcome difficulty caused by multicollinearity but also resist the influence of outliers.