Mean squared error matrix comparisons of some biased estimators in linear regression

Akdeniz F., Erol H.

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, cilt.32, sa.12, ss.2389-2413, 2003 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 32 Sayı: 12
  • Basım Tarihi: 2003
  • Doi Numarası: 10.1081/sta-120025385
  • Dergi Adı: COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2389-2413
  • Çukurova Üniversitesi Adresli: Hayır

Özet

Consider the linear regression model y = Xbeta + it in the usual notation. In the presence of multicollinearity certain biased estimators like the ordinary ridge regression estimator (β) over cap (k) = (X'X + kI)X-1'y and the Liu estimator (β) over cap (d) = (X'X + I)(-1)(X'y + d (β) over cap) introduced by Liu (Liu, Ke Jian. (1993). A new class of biased estimate in linear regression. Communications in Statistics- Theory and Methods 22(2):393-402) or improved ridge and Liu estimators are used to out-perform the ordinary least squares estimates in the linear regression model. In this article we compare the (almost unbiased) generalized ridge regression estimator with the (almost unbiased) generalized Liu estimator in the matrix mean square error sense.