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This paper presents a fast methodology, called ROBOUT, to identify outliersin a response variable conditional on a set of linearly related predictors,retrieved from a large granular dataset. ROBOUT is shown to be effective andparticularly versatile compared to existing methods in the presence of a numberof data idiosyncratic features. ROBOUT is able to identify observations withoutlying conditional variance when the dataset contains element-wise sparsevariables, and the set of predictors contains multivariate outliers. Existingintegrated methodologies like SPARSE-LTS and RLARS are systematicallysub-optimal under those conditions. ROBOUT entails a robust selection stage ofthe statistically relevant predictors (by using a Huber or a quantile loss),the estimation of a robust regression model based on the selected predictors(by LTS, GS or MM), and a criterion to identify conditional outliers based on arobust measure of the residuals' dispersion. We conduct a comprehensivesimulation study in which the different variants of the proposed algorithm aretested under an exhaustive set of different perturbation scenarios. Themethodology is also applied to a granular supervisory banking dataset collectedby the European Central Bank.

Robust selection of predictors and conditional outlier detection in a perturbed large-dimensional regression context