More on the restricted ridge regression estimation

Several alternative methods for derivation of the restricted ridge regression estimator (RRRE) are provided. Theoretical comparison and relationship of RRRE with related methods for regression with the multicollinearity problem are described. We also find inter-connections among RRRE, ordinary ridge regression estimator (ORRE), restricted least squares estimator (RLSE), modified ridge regression estimator (MRRE) and restricted modified generalized ridge estimator (RMGRE). Finally, numerical comparison, in addition to theoretical derivation, is also conducted with a Monte Carlo simulation and a real data example.

[1]  E. Liski,et al.  Necessary and sufficient conditions for superiority of misspecified restricted least squares regression estimator , 1998 .

[2]  A. E. Hoerl,et al.  Ridge regression:some simulations , 1975 .

[3]  G. C. McDonald,et al.  A Monte Carlo Evaluation of Some Ridge-Type Estimators , 1975 .

[4]  Guy Lebanon,et al.  Linear Regression , 2010 .

[5]  Felix Famoye,et al.  Improving Efficiency by Shrinkage , 1999, Technometrics.

[6]  A. E. Hoerl,et al.  Ridge regression: biased estimation for nonorthogonal problems , 2000 .

[7]  M. Revan Özkale.  Comment on Ridge Estimation to the Restricted Linear Model , 2009 .

[8]  F. Akdeniz,et al.  Mean squared error comparisons of the modified ridge regression estimator and iiie restricted ridge regression estimator , 1998 .

[9]  The restricted least squares estimator and ridge regression , 1984 .

[10]  Jeffrey Pliskin.  A ridge-type estimator and good prior means , 1987 .

[11]  Jürgen Groß.  Restricted ridge estimation , 2003 .

[12]  B. F. Swindel.  Good ridge estimators based on prior information , 1976 .

[13]  Hu Yang,et al.  Ridge Estimation to the Restricted Linear Model , 2007 .

[14]  Nityananda Sarkar,et al.  A new estimator combining the ridge regression and the restricted least squares methods of estimation , 1992 .

[15]  On ecological regression and ridge estimation , 1995 .

[16]  Kejian Liu.  Using Liu-Type Estimator to Combat Collinearity , 2003 .

[17]  Hamza Erol,et al.  Mean Squared Error Matrix Comparisons of Some Biased Estimators in Linear Regression , 2003 .

[18]  Selahattin Kaçiranlar,et al.  A Comparison of Mixed and Ridge Estimators of Linear Models , 2009, Commun. Stat. Simul. Comput..

[19]  Jürgen Gross,et al.  Linear Regression , 2003 .

[20]  Dale Borowiak,et al.  Linear Models, Least Squares and Alternatives , 2001, Technometrics.

[21]  Götz Trenkler,et al.  Mean squared error matrix comparisons between biased estimators — An overview of recent results , 1990 .