  This paper presents a fast methodology, called ROBOUT, to identify outliers
in a response variable conditional on a set of linearly related predictors,
retrieved from a large granular dataset. ROBOUT is shown to be effective and
particularly versatile compared to existing methods in the presence of a number
of data idiosyncratic features. ROBOUT is able to identify observations with
outlying conditional variance when the dataset contains element-wise sparse
variables, and the set of predictors contains multivariate outliers. Existing
integrated methodologies like SPARSE-LTS and RLARS are systematically
sub-optimal under those conditions. ROBOUT entails a robust selection stage of
the 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 a
robust measure of the residuals' dispersion. We conduct a comprehensive
simulation study in which the different variants of the proposed algorithm are
tested under an exhaustive set of different perturbation scenarios. The
methodology is also applied to a granular supervisory banking dataset collected
by the European Central Bank.
