On a robust estimator in heteroscedastic regression model in the presence of outliers

The ordinary least squares (OLS) procedure is inefficient when the underlying assumption of constant error variances (homoscedasticity) is not met. As an alternative, we often used weighted least squares (WLS) procedure which requires a known form of the heteroscedastic errors structures, to estimate the regression parameters when heteroscedasticity occurs in the data. It is now evident that the WLS estimator is easily affected by outliers. To remedy the problem of heteroscedasticity and outliers simultaneously, we proposed a new method that we call two-step robust weighted least squares (TSRWLS) where prior information on the structure of the heteroscedastic errors is not required. The performance of the newly proposed estimator is investigated extensively by real data sets and Monte Carlo simulations.