The restricted and unrestricted two-parameter estimators


Oezkale M. R. , KAÇIRANLAR S.

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, cilt.36, ss.2707-2725, 2007 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 36
  • Basım Tarihi: 2007
  • Doi Numarası: 10.1080/03610920701386877
  • Dergi Adı: COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
  • Sayfa Sayıları: ss.2707-2725

Özet

In this article, we introduce a new two-parameter estimator by grafting the contraction estimator into the modified ridge estimator proposed by Swindel (1976). This new two-parameter estimator is a general estimator which includes the ordinary least squares, the ridge, the Liu, and the contraction estimators as special cases. Furthermore, by setting restrictions R beta = r on the parameter values we introduce a new restricted two-parameter estimator which includes the well-known restricted least squares, the restricted ridge proposed by Gro beta (2003), the restricted contraction estimators, and a new restricted Liu estimator which we call the modified restricted Liu estimator different from the restricted Liu estimator proposed by Kaciranlar et al. (1999). We also obtain necessary and sufficient condition for the superiority of the new two-parameter estimator over the ordinary least squares estimator and the comparison of the new restricted two-parameter estimator to the new two-parameter estimator is done by the criterion of matrix mean square error. The estimators of the biasing parameters are given and a simulation study is done for the comparison as well as the determination of the biasing parameters.

In this article, we introduce a new two-parameter estimator by grafting the contraction estimator into the modified ridge estimator proposed by Swindel (1976). This new two-parameter estimator is a general estimator which includes the ordinary least squares, the ridge, the Liu, and the contraction estimators as special cases. Furthermore, by setting restrictions Rβ = r on the parameter values we introduce a new restricted two-parameter estimator which includes the well-known restricted least squares, the restricted ridge proposed by Groß (2003), the restricted contraction estimators, and a new restricted Liu estimator which we call the modified restricted Liu estimator different from the restricted Liu estimator proposed by Kaçıranlar et al. (1999). We also obtain necessary and sufficient condition for the superiority of the new two-parameter estimator over the ordinary least squares estimator and the comparison of the new restricted two-parameter estimator to the new two-parameter estimator is done by the criterion of matrix mean square error. The estimators of the biasing parameters are given and a simulation study is done for the comparison as well as the determination of the biasing parameters.