Abstract
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.
Highlights
Tukey (1979) recommends that it is perfectly proper to routinely use both the ordinary least squares (OLS) and robust estimators and only examine the data more closely in case of “large” discrepancies-whatever this means
The main reason why this status quo remains is that at the interface of statistics and its applications there are non-specialists who find it insurmountable to deal with this vague idea of “large” discrepancies and the necessary choices of types of estimators and tuning constants involved in the robust statistical methodology
The focus of this paper is to contribute by adding some new outlier diagnostics to the few existing ones in the regression quantiles (RQs) framework and further bring in the OLS’s attractiveness to this framework via studentization of residual statistics
Summary
Tukey (1979) recommends that it is perfectly proper to routinely use both the ordinary least squares (OLS) and robust estimators and only examine the data more closely in case of “large” discrepancies-whatever this means (but it is widely accepted that this means that otherwise it suffices to use the OLS). The focus of this paper is to contribute by adding some new outlier diagnostics to the few existing ones in the RQ framework and further bring in the OLS’s attractiveness to this framework via studentization of residual statistics. A studentized residual statistics are suggested for RQs here based on the ES method.
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