The problem of estimation of the regression coefficients under multicollinearity situation for the restricted linear model is discussed. Some improve estimators are considered, including the unrestricted ridge regression estimator (URRE), restricted ridge regression estimator (RRRE), shrinkage restricted ridge regression estimator (SRRRE), preliminary test ridge regression estimator (PTRRE), and restricted Liu estimator (RLIUE). The were compared based on the sampling variance-covariance criterion. The RRRE dominates other ridge estimators when the restriction does or does not hold. A numerical example was provided. The RRRE performed equivalently or better than the RLIUE in the sense of having smaller sampling variance.
Kibria, B. M. Golam
"Applications of Some Improved Estimators in Linear Regression,"
Journal of Modern Applied Statistical Methods: Vol. 5
, Article 11.
Available at: http://digitalcommons.wayne.edu/jmasm/vol5/iss2/11