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 ...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.展开更多
In this paper, a class of new biased estimators for linear model is proposed by modifying the singular values of the design matrix so as to directly overcome the difficulties caused by ill_conditioning in the design m...In this paper, a class of new biased estimators for linear model is proposed by modifying the singular values of the design matrix so as to directly overcome the difficulties caused by ill_conditioning in the design matrix. Some important properties of these new estimators are obtained. By appropriate choices of the biased parameters, we construct many useful and important estimators. An application of these new estimators in three_dimensional position adjustment by distance in a spatial coordiate surveys is given. The results show that the proposed biased estimators can effectively overcome ill_conditioning and their numerical stabilities are preferable to ordinary least square estimation.展开更多
文摘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.
文摘In this paper, a class of new biased estimators for linear model is proposed by modifying the singular values of the design matrix so as to directly overcome the difficulties caused by ill_conditioning in the design matrix. Some important properties of these new estimators are obtained. By appropriate choices of the biased parameters, we construct many useful and important estimators. An application of these new estimators in three_dimensional position adjustment by distance in a spatial coordiate surveys is given. The results show that the proposed biased estimators can effectively overcome ill_conditioning and their numerical stabilities are preferable to ordinary least square estimation.
