Abstract
In this paper we compare recently developed preliminary test estimator called Preliminary Test Stochastic Restricted Liu Estimator (PTSRLE) with Ordinary Least Square Estimator (OLSE) and Mixed Estimator (ME) in the Mean Square Error Matrix (MSEM) sense for the two cases in which the stochastic restrictions are correct and not correct. Finally a numerical example and a Monte Carlo simulation study are done to illustrate the theoretical findings.
Highlights
To overcome the multicollinearity problem arises in the Ordinary Least Squares Estimation (OLSE) procedure, different methods have been proposed in the literature
Theorem 1: 1) When the stochastic restrictions are true (i.e. δ = 0 ), the Preliminary Test Stochastic Restricted Liu Estimator (PTSRLE) is superior to OLSE in the mean square error matrix sense if and only if d1*′D1*−1d1* ≤ 1, where d1* =(d −1)( S + I )−1 β, ( ) D1* = σ 2S −1 − σ 2 Fd S −1Fd′ + σ 2hλ* 2 Fd GFd′, and hλ∗ (2) is the value of hλ (2) when δ = 0
The PTSRLE is superior to OLSE in the mean square error matrix sense when stochastic restrictions are correct if and only if d1*′D1*−1d1* ≤ 1
Summary
To overcome the multicollinearity problem arises in the Ordinary Least Squares Estimation (OLSE) procedure, different methods have been proposed in the literature. By combining OLSE and ME, the Ordinary Stochastic Preliminary Test Estimator (OSPE) was proposed by Wijekoon [8]. Arumairajan and Wijekoon [9] introduced the Preliminary Test Stochastic Restricted Liu Estimator (PTSRLE) by combining the Stochastic Restricted Liu Estimator and Liu Estimator. In their study, they compared PTSRLE with SRLE by using the Mean Square Error Matrix (MSEM) and Scalar Mean Square Error (SMSE) criterions. A numerical example and a Monte Carlo simulation are used to illustrate the theoretical findings in section 4, and in section 5 we state the conclusions
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