Reliable Robust Regression Diagnostics

Abstract

Motivated by the requirement of controlling the number of false discoveries that arises in several application fields, we study the behaviour of diagnostic procedures obtained from popular highbreakdown regression estimators when no outlier is present in the data. We find that the empirical error rates for many of the available techniques are surprisingly far from the prescribed nominal level. Therefore, we propose a simulation-based approach to correct the liberal diagnostics and reach reliable inferences. We provide evidence that our approach performs well in a wide range of settings of practical interest and for a variety of robust regression techniques, thus showing general appeal. We also evaluate the loss of power that can be expected from our corrections under different contamination schemes and show that this loss is often not dramatic. Finally, we detail some possible extensions that may further enhance the applicability of the method.

Robust Regression with Density Power Divergence: Theory, Comparisons, and Data Analysis

“…These results also implicitly show that the choice of the function is not a crucial aspect since all (provided they are bounded) have similar behavior in terms of breakdown point and efficiency. These theoretical results are in line with the empirical findings in Salini et al [ 18 ], where it is shown that the size of the test for outlier detection is much more affected by the choice of the requested level of efficiency or breakdown point than by the choice of the function.…”

The power of monitoring: how to make the most of a contaminated multivariate sample

“…As a consequence, frequent examples can be found that use numerical and graphical inspection of robust residuals in regression and of robust Mahalanobis distances with multivariate data; see, e.g., Hubert et al (2008) for an overview. Cerioli et al (2009), Cerioli (2010) and Salini et al (2016) show how to calibrate the robust diagnostics in order to obtain valid inferential conclusions in the case of small and moderate sample sizes, when asymptotic results are not reliable, thus enhancing their practical usefulness. Modern developments include the bagdistance map of Hubert et al (2015) for the identification of multivariate functional outliers, regularized versions of the robust diagnostics to be used when the number of variables is large with respect to the sample size (Alfons et al, 2013;Boudt et al, 2017;Atkinson et al, 2017a) and extensions to non-normal models (Agostinelli et al, 2014;Amiguet et al, 2017).…”

Robust multivariate analysis for mixed-type data: Novel algorithm and its practical application in socio-economic research

“…The key difference with respect to other robust strategies for data analysis, is that the algorithm is not only based on one subsample, but on a sequence of subsets of the original data. It is an adaptive hard trimming method (Salini et al, 2016). In the words of their initial proponents "the FS is not a simple new algorithm but a new philosophy of looking at the data, which involves watching a film of the data rather than a snapshot".…”