Predictive Performance Evaluation of the Kibria-Lukman Estimator

Abstract

Regression models are commonly used in prediction, but their predictive performances may be affected by the problem called the multicollinearity. To reduce the effect of the multicollinearity, different biased estimators have been proposed as alternatives to the ordinary least squares estimator. But there are still little analyses of the different proposed biased estimators’ predictive performances. Therefore, this paper focuses on discussing the predictive performance of the recently proposed “new ridge-type estimator”, namely the Kibria-Lukman (KL) estimator. The theoretical comparisons among the predictors of these estimators are done according to the prediction mean squared error criterion in the two-dimensional space and the results are explained by a numerical example. The regions are determined where the KL estimator gives better results than the other estimators.

On the biased Two-Parameter Estimator to Combat Multicollinearity in Linear Regression Model

“…OLS produces unbiased but inefficient estimates of the model parameters [3]. Biased estimators such as Stein estimator [4], Principal Component estimator [5], Partial Least Square estimator [6], Ridge regression estimator [7], Liu estimator [8], modified ridge regression estimator [9], two-parameter (TP) estimator [10], KL estimator [11], DK estimator [12], proposed two-parameter estimator [13], Liu-Dawoud-Kibria estimator [14], New ridge-type estimator [15], Generalized Kibria-Lukman estimator [16], Tobit new ridge-type [17] and others are often used to address this problem.…”