A new ridge-type estimator in stochastic restricted linear regression

Abstract

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, Weighted mixed regression, Zeitschrift fur Angewandte Mathematik und Mechanik 70 (1990), pp. 735–738] and ordinary ridge estimator (ORE) [A.E. Hoerl and R.W. Kennard, Ridge regression: Biased estimation for non-orthogonal problems, Technometrics 12 (1970), pp. 55–67]. The performances of this new estimator against the weighted mixed estimator, ORE and the mixed ridge estimator [Y.L. Li and H. Yang, A new stochastic mixed ridge estimator in linear regression, Stat. Pap. (2008) (in press, DOI 10.1007/s00362-008-0169-5)] 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.

Keywords:

• weighted mixed ridge estimator
• ordinary ridge estimator
• weighted mixed estimator
• mixed ridge estimator
• mean squared error matrix

2000 Mathematics Subject Classification :

• 62J05
• 62J07

Acknowledgements

The authors are most grateful to the anonymous reviewer for his valuable comments and suggestions that helped them improve the presentation of the article. The research was supported by Natural Science Foundation Project of CQ CSTC (2009BB6189).