Combining Random and Specific Directions for Outlier Detection and Robust Estimation in High-Dimensional Multivariate Data

A powerful procedure for outlier detection and robust estimation of shape and location with multivariate data in high dimension is proposed. The procedure searches for outliers in univariate projections on directions that are obtained both randomly, as in the Stahel-Donoho method, and by maximizing and minimizing the kurtosis coefficient of the projected data, as in the Peña and Prieto method. We propose modifications of both methods to improve their computational efficiency and combine them in a procedure which is affine equivariant, has a high breakdown point, is fast to compute and can be applied when the dimension is large. Its performance is illustrated with a Monte Carlo experiment and in a real dataset.