ROBOUT: a conditional outlier detection methodology for high-dimensional data

Abstract This paper presents a methodology, called ROBOUT, to identify outliers conditional on a high-dimensional noisy information set. In particular, ROBOUT is able to identify observations with outlying conditional mean or variance when the dataset contains multivariate outliers in or besides the predictors, multi-collinearity, and a large variable dimension compared to the sample size. ROBOUT entails a pre-processing step, a preliminary robust imputation procedure that prevents anomalous instances from corrupting predictor recovery, a selection stage of the statistically relevant predictors (through cross-validated LASSO-penalized Huber loss regression), the estimation of a robust regression model based on the selected predictors (via MM regression), and a criterion to identify conditional outliers. We conduct a comprehensive simulation study in which the proposed algorithm is tested under a wide range of perturbation scenarios. The combination formed by LASSO-penalized Huber loss and MM regression turns out to be the best in terms of conditional outlier detection under the above described perturbed conditions, also compared to existing integrated methodologies like Sparse Least Trimmed Squares and Robust Least Angle Regression. Furthermore, the proposed methodology is applied to a granular supervisory banking dataset collected by the European Central Bank, in order to model the total assets of euro area banks.