Quality of fit measurement in regression quantiles: An elemental set method approach

On studentized residuals in the quantile regression framework

Although regression quantiles (RQs) are increasingly becoming popular, they are still playing a second fiddle role to the ordinary least squares estimator like their robust counterparts due to the perceived complexity of the robust statistical methodology. In order to make them attractive to statistical practitioners, an endeavor to studentize robust estimators has been undertaken by some researchers. This paper suggests two versions of RQs studentized residual statistics, namely, internally and externally studentized versions based on the elemental set method. The more preferred externally studentized version is compared to the one based on standardized median absolute deviation (MAD) of residuals using a well-known data set in the literature. While the MAD based outlier diagnostic seemed to be uniform and more aggressive to flagging outliers the RQ externally studentized one exhibited a dynamic pattern consistent with RQ results.