A stochastic restricted k–d class estimator

Abstract

In this paper, we introduce a stochastic restricted k–d class estimator for the vector of parameters in a linear model when additional linear restrictions on the parameter vector are assumed to hold. The stochastic restricted k–d class estimator is a generalization of the ordinary mixed estimator and the k–d class estimator. We show that our new biased estimator is superior in the mean squared error matrix sense to the k–d class estimator [S. Sakallıoğlu and S. Kaçiranlar, A new biased estimator based on ridge estimation, Statist. Papers 49 (2008), pp. 669–689] and the stochastic restricted Liu estimator [H. Yang and J.W. Xu, An alternative stochastic restricted Liu estimator in linear regression, Statist. Papers 50 (2009), pp. 639–647]. Finally, a numerical example is given to show the theoretical results.

Keywords:

• ordinary least squares estimator
• ordinary mixed estimator
• k–d class estimator
• stochastic restricted Liu estimator
• mean squared error matrix

2000 Mathematics Subject Classification :

• 62J07
• 62F30

Acknowledgements

The authors would like to thank the anonymous referee and the editor for their constructive criticism which significantly improved the presentation of the article.