Outlier detection in high-dimensional datasets poses new challenges that have not been investigated in the literature. In this paper, we present an integrated methodology for the identification of outliers which is suitable for datasets with higher number of variables than observations. Our method aims to utilise the entire relevant information present in a dataset to detect outliers in an automatized way, a feature that renders the method suitable for application in large dimensional datasets. Our proposed five-step procedure for regression outlier detection entails a robust selection stage of the most explicative variables, the estimation of a robust regression model based on the selected variables, and a criterion to identify outliers based on robust measures of the residuals' dispersion. The proposed procedure deals also with data redundancy and missing observations which may inhibit the statistical processing of the data due to the ill-conditioning of the covariance matrix. The method is validated in a simulation study and an application to actual supervisory data on banks' total assets.
Outlier detection Robust regression Variable selection High dimension Missing data Banking data