Statistical Papers

, Volume 51, Issue 3, pp 651–672 | Cite as

Simulation study of new estimators combining the SUR ridge regression and the restricted least squares methodologies

  • M. A. AlkhamisiEmail author
Regular Article


In this paper, we propose two SUR type estimators based on combining the SUR ridge regression and the restricted least squares methods. In the sequel these estimators are designated as the restricted ridge Liu estimator and the restricted ridge HK estimator (see Liu in Commun Statist Thoery Methods 22(2):393–402, 1993; Sarkar in Commun Statist A 21:1987–2000, 1992). The study has been made using Monte Carlo techniques, (1,000 replications), under certain conditions where a number of factors that may effect their performance have been varied. The performance of the proposed and some of the existing estimators are evaluated by means of the TMSE and the PR criteria. Our results indicate that the proposed SUR restricted ridge estimators based on K SUR, K Sratio, K Mratio and \({\ddot{K}}\) produced smaller TMSE and/or PR values than the remaining estimators. In contrast with other ridge estimators, components of \({\ddot{K}}\) are defined in terms of the eigenvalues of \({X^{{\ast^{\prime}}} X^{\rm \ast}}\) and all lie in the open interval (0, 1).


Multicollinearity Restricted generalized least squares estimator SUR restricted ridge estimator Liu estimator Biased estimator Monte Carlo simulation 

Mathematics Subject Classification (2000)



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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Centre for Labor Market Policy (CAFO), Department of Economics and StatisticsVäxjö UniversityVäxjöSweden

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