Superiority of the r-k Class Estimator Over Some Estimators In A Linear Model

Siray G., SAKALLIOĞLU S.

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, cilt.41, sa.15, ss.2819-2832, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 15
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1080/03610926.2011.648786
  • Dergi Adı: COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2819-2832
  • Anahtar Kelimeler: Average loss criterion, r - k Class estimator, Mahalanobis loss function, Principal components regression estimator, Ridge regression estimator, PRINCIPAL COMPONENT REGRESSION, RIDGE-REGRESSION, COMBINING RIDGE
  • Çukurova Üniversitesi Adresli: Evet

Özet

In regression analysis, to overcome the problem of multicollinearity, the r - k class estimator is proposed as an alternative to the ordinary least squares estimator which is a general estimator including the ordinary ridge regression estimator, the principal components regression estimator and the ordinary least squares estimator. In this article, we derive the necessary and sufficient conditions for the superiority of the r - k class estimator over each of these estimators under the Mahalanobis loss function by the average loss criterion. Then, we compare these estimators with each other using the same criterion. Also, we suggest to test to verify if these conditions are indeed satisfied. Finally, a numerical example and a Monte Carlo simulation are done to illustrate the theoretical results.