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.