Robust estimation and variable selection in heteroscedastic regression model using least favorable distribution

The assumption of equal variances is not always appropriate and different approaches for modelling variance heterogeneity have been widely studied in the literature. One of these approaches is joint location and scale model defined with the idea that both the location and the scale depend on explanatory variables through parametric linear models. Because the joint location and scale model includes two models, it does not deal well with a large number of irrelevant variables. Therefore, determining the variables that are important for the location and the scale is as important as estimating the parameters of these models. From this point of view, a combine robust estimation and variable selection method is proposed to simultaneously estimate the parameters and select the important variables. This is done using the least favorable distribution and least absolute shrinkage and selection operator method. Under appropriate conditions, we study the consistency, asymptotic distribution and the sparsity property of the proposed robust estimator. Simulation studies and a real data example are provided to demonstrate the advantages of the proposed method over existing methods in literature.