A novel Bayesian framework to address unknown heteroscedasticity for the linear regression model

A common problem that we encounter in linear regression models is that the error variances are not the same for all the observations, that is, there is an issue of heteroscedasticity. To avoid the adverse effects of this issue on the estimates obtained by the ordinary least squares, it is a usual practice to use the estimated weighted least squares (EWLS) method or to use some adaptive methods, especially when the form of heteroscedasticity is unknown. The current article proposes a novel Bayesian version of the EWLS estimator. The performance of the proposed estimator has been evaluated in terms of its efficiency using the Monte Carlo simulations. An example has also been included for the demonstration.