Properties of some new preliminary test Liu estimators and comparisons with the usual preliminary test estimators
G. Yuksel and F. Akdeniz (2001). Properties of some new preliminary test Liu estimators and comparisons with the usual preliminary test estimators. Journal of Statistical Research, Vol. 35, No. 2, pp. 45-56.
Abstract
This paper deals with the standard multiple regression model $(Y, X\beta,\sigma^2I)$ under multicollinearity situation. We introduce a new biased estimator for $\beta$ and discuss its properties in some detail. This new estimator combines the idea of preliminary test and characteristics of the new biased estimator introduced by Liu (1993). So the unrestricted Liu estimator (URLE), restricted Liu estimator (RLE) and finally the preliminary test Liu estimator (PTLE) are considered. The bias, variance-covariance matrix and mean square error (mse) of the new estimator is derived and compared with the usual preliminary test estimator (PTE).