Abstract
Ridge type estimators are used to estimate regression parameters in a multiple linear regression model when multicolinearity exists among predictor variables. When different estimators are available, preliminary test estimation procedure is adopted to select a suitable estimator. In this paper, two ridge estimators, the Stochastic Restricted Liu Estimator and Liu Estimator are combined to define a new preliminary test estimator, namely the Preliminary Test Stochastic Restricted Liu Estimator (PTSRLE). The stochastic properties of the proposed estimator are derived, and the performance of PTSRLE is compared with SRLE in the sense of mean square error matrix (MSEM) and scalar mean square error (SMSE) for the two cases in which the stochastic restrictions are correct and not correct. Moreover the SMSE of PTSRLE based on Wald (WA), Likelihood Ratio (LR) and Lagrangian Multiplier (LM) tests are derived, and the performance of PTSRLE is compared using WA, LR and LM tests as a function of the shrinkage parameter d with respect to the SMSE. Finally a numerical example is given to illustrate some of the theoretical findings.
Highlights
A common problem in a multiple linear regression model is a multicolllinearity
The scalar mean square error (SMSE) of Preliminary Test Stochastic Restricted Liu Estimator (PTSRLE) based on Wald (WA), Likelihood Ratio (LR) and Lagrangian Multiplier (LM) tests are derived, and the performance of PTSRLE is compared using WA, LR and LM tests as a function of the shrinkage parameter d with respect to the SMSE
We summarize our findings: Theorem 3.2: 1) If the stochastic restrictions are true (i.e. 0 ); the Stochastic Restricted Liu Estimator (SRLE) is always superior to the PTSRLE in the scalar mean squared error sense
Summary
A common problem in a multiple linear regression model is a multicolllinearity. Some biased estimators are proposed to solve this problem such as the Ordinary Ridge Estimator (ORE) by Hoerl and Kennard [1], the Restricted Ridge Estimator (RRE) by Sarkar [2], the Liu Estimator (LE) by Liu [3], the Restricted Liu Estimator (RLE) by Kaçiranlar, et al [4] and the Stochastic Restricted Liu Estimator (SRLE) by Hubert and Wijekoon [5]. Yang and Xu [14] have introduced the preliminary test Liu estimators based on these three tests by combining the Restricted Liu Estimator (RLE) and the Liu Estimator. We illustrated these comparisons with a numerical example
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
