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Research on the biased estimators of coefficients in linear regression models. (Chinese. English summary) Zbl 1260.62060

Summary: Aiming at the fundamental reason for the bad performance of the LS estimator of the coefficients in linear regression models, this paper presents the generalized c-K estimators of the coefficients, which combines various classical biased estimators into a bigger class of estimators and studies the improvement of the biased estimators. It is proved that the Stein estimators can be improved by minimizing the mean square error of the generalized c-K estimators or by specializing the matrix K, respectively, and the optimal values of the parameters are also obtained. The proposed approach provides an effective way to the improvement of the biased estimators of the coefficients in linear regression models.

MSC:

62J07 Ridge regression; shrinkage estimators (Lasso)
62F10 Point estimation
62J05 Linear regression; mixed models