Abstract
The parameter estimation problem in Gauss-Markov model is considered when multi-collinearity and outliers exist simultaneously. A class of new estimators, robust-type generalized shrunken estimators, is proposed by grafting robust estimation technique into philosophy generalized shrunken estimation. Many useful and important estimators such as robust-type ordinary ridge estimator, robust-type principal components estimator and so on are obtained by appropriate choices of the shrinking parameter matrix. An algorithm for computing the robust-type generalized shrunken estimate is established. A numerical example is provided to illustrate that these new estimators can not only effectively overcome difficulty caused by multi-collinearity but also resist the influence of outliers.
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