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A new ridge-type estimator in stochastic restricted linear regression. (English) Zbl 1283.62145

Summary: In this paper, we propose a new ridge-type estimator called the weighted mixed ridge estimator by unifying the sample and prior information in linear model with additional stochastic linear restrictions. The new estimator is a generalization of the weighted mixed estimator [B. Schaffrin and H. Toutenburg, Z. Angew. Math. Mech. 70, No. 6, 735–738 (1990; Zbl 0714.62061)] and ordinary ridge estimator (ORE) [A. E. Hoerl and R. W. Kennard, Technometrics 12, 55–67 (1970; Zbl 0202.17205)]. The performances of this new estimator against the weighted mixed estimator, ORE and the mixed ridge estimator [Y. Li and H. Yang, Stat. Pap. 51, No. 2, 315–323 (2010; Zbl 1247.62179)] are examined in terms of the mean squared error matrix sense. Finally, a numerical example and a Monte Carlo simulation are also given to show the theoretical results.

MSC:

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