Comparisons of the r-k class estimator to the ordinary least squares estimator under the Pitman's closeness criterion


Ozkale M. R. , KAÇIRANLAR S.

STATISTICAL PAPERS, cilt.49, ss.503-512, 2008 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 49 Konu: 3
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1007/s00362-006-0029-0
  • Dergi Adı: STATISTICAL PAPERS
  • Sayfa Sayısı: ss.503-512

Özet

In the presence of multicollinearity, the r - k class estimator is proposed as an alternative to the ordinary least squares (OLS) estimator which is a general estimator including the ordinary ridge regression (ORR), the principal components regression (PCR) and the OLS estimators. Comparison of competing estimators of a parameter in the sense of mean square error (MSE) criterion is of central interest. An alternative criterion to the MSE criterion is the Pitman's (1937) closeness (PC) criterion. In this paper, we compare the r - k class estimator to the OLS estimator in terms of PC criterion so that we can get the comparison of the ORR estimator to the OLS estimator under the PC criterion which was done by Mason et al. (1990) and also the comparison of the PCR estimator to the OLS estimator by means of the PC criterion which was done by Lin and Wei (2002).

In the presence of multicollinearity, the r − k class estimator is proposed as an alternative to the ordinary least squares (OLS) estimator which is a general estimator including the ordinary ridge regression (ORR), the principal components regression (PCR) and the OLS estimators. Comparison of competing estimators of a parameter in the sense of mean square error (MSE) criterion is of central interest. An alternative criterion to the MSE criterion is the Pitman’s (1937) closeness (PC) criterion. In this paper, we compare the r − k class estimator to the OLS estimator in terms of PC criterion so that we can get the comparison of the ORR estimator to the OLS estimator under the PC criterion which was done by Mason et al. (1990) and also the comparison of the PCR estimator to the OLS estimator by means of the PC criterion which was done by Lin and Wei (2002).