Weighted validation of heteroscedastic regression models for better selection

In this paper, we suggest a method for improving model selection in the presence of heteroscedasticity. For this purpose, we measure the heteroscedasticity in the data using the inter-quartile range (IQR) of the fitted values under the framework of cross-validation. To find the IQR, we fit 0.25 and 0.75 generic quantile regression using the training data. The two models then predict the values of the response variable at 0.25 and 0.75 quantiles in the test data, which yields predicted IQR. To reduce the effect of heteroscedastic data in the model selection, we propose to use weighted prediction error. The inverse of the predicted IQR is utilized to estimate the weights. The proposed method reduces the impact of large prediction errors via weighted prediction and leads to better model and parameter selection. The benefits of the proposed method are demonstrated in simulations and with two real data sets.