The relative efficiency of the restricted estimators in linear regression models


Ozkale M. R.

JOURNAL OF APPLIED STATISTICS, cilt.41, sa.5, ss.998-1027, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 5
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1080/02664763.2013.859234
  • Dergi Adı: JOURNAL OF APPLIED STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.998-1027
  • Anahtar Kelimeler: linear restrictions, restricted ridge regression estimator, restricted least squares estimator, mean square error, restricted two parameter estimator, RIDGE-REGRESSION, LEAST-SQUARES, BIASED-ESTIMATION, SELECTION, VARIABLES
  • Çukurova Üniversitesi Adresli: Evet

Özet

This paper deals with the problem of multicollinearity in a multiple linear regression model with linear equality restrictions. The restricted two parameter estimator which was proposed in case of multicollinearity satisfies the restrictions. The performance of the restricted two parameter estimator over the restricted least squares (RLS) estimator and the ordinary least squares (OLS) estimator is examined under the mean square error (MSE) matrix criterion when the restrictions are correct and not correct. The necessary and sufficient conditions for the restricted ridge regression, restricted Liu and restricted shrunken estimators, which are the special cases of the restricted two parameter estimator, to have a smaller MSE matrix than the RLS and the OLS estimators are derived when the restrictions hold true and do not hold true. Theoretical results are illustrated with numerical examples based on Webster, Gunst and Mason data and Gorman and Toman data. We conduct a final demonstration of the performance of the estimators by running a Monte Carlo simulation which shows that when the variance of the error term and the correlation between the explanatory variables are large, the restricted two parameter estimator performs better than the RLS estimator and the OLS estimator under the configurations examined.