A Bootstrap Study of Variance Estimation under Heteroscedasticity Using Genetic Algorithm

Abstract

The conventional ordinary least squares (OLS) variance-covariance matrix estimator for a linear regression model under heteroscedastic errors is biased and inconsistent. Accordingly, several estimators have so far been proposed by various researchers. However, none of these perform well under the finite-sample situation. In this paper, the powerful optimization technique of Genetic algorithm (GA) is used to modify these estimators. Properties of these newly developed estimators are thoroughly studied by Monte Carlo method for various sample sizes. It is shown that GA-versions of the estimators are superior to corresponding non-GA versions as there are significant reductions in the Total relative bias as well as Total root mean square error.

Key Words:

• Linear regression model
• Least squares estimators
• Heteroscedasticity
• Real-coded genetic algorithm
• Bootstrap methods
• Total relative bias
• Total root mean square error