Fast algorithms for the minimum volume estimator

The minimum volume ellipsoid (MVE) estimator is an important tool in robust regression and outlier detection in statistics. We develop fast and efficient algorithms for the MVE estimator problem and discuss how they can be implemented efficiently. The novelty of our approach stems from the recent developments in the first‐order algorithms for solving the related minimum volume enclosing ellipsoid problem. Comparative computational results are provided which demonstrate the strength of the algorithms.