Performance of Kibria's Method for the Heteroscedastic Ridge Regression Model: Some Monte Carlo Evidence

Abstract

It is common for a linear regression model that the error terms display some form of heteroscedasticity and at the same time, the regressors are also linearly correlated. Both of these problems have serious impact on the ordinary least squares (OLS) estimates. In the presence of heteroscedasticity, the OLS estimator becomes inefficient and the similar adverse impact can also be found on the ridge regression estimator that is alternatively used to cope with the problem of multicollinearity. In the available literature, the adaptive estimator has been established to be more efficient than the OLS estimator when there is heteroscedasticity of unknown form. The present article proposes the similar adaptation for the ridge regression setting with an attempt to have more efficient estimator. Our numerical results, based on the Monte Carlo simulations, provide very attractive performance of the proposed estimator in terms of efficiency. Three different existing methods have been used for the selection of biasing parameter. Moreover, three different distributions of the error term have been studied to evaluate the proposed estimator and these are normal, Student's t and F distribution.

Keywords:

• Adaptive estimator
• Kernel estimator
• Multicollinearity
• Ridge regression

AMS Subject Classification:

• 62J07
• 62J05
• 62F03

Acknowledgments

I gratefully acknowledge the Higher Education Commission (HEC) of Pakistan for granting me a Post-Doctoral Fellowship to peruse the current research work. I also wish to thank Prof. Hervé Cardot, Insitut de Mathématiques de Bourgogne (IMB), Dijon, France, for hosting me in the Postdoctoral Program and for his guidance and fruitful comments.