Fast highly efficient and robust one-step MM-estimators of scale based on QnQn

A parametric family of MM-estimators of scale based on the Rousseeuw–Croux QnQn-estimator is proposed; estimator’s bias and efficiency are studied. A low-complexity one-step MM-estimator is obtained allowing a considerably faster computation with greater than 80% efficiency and the highest possible 50% breakdown point. Analytical and Monte Carlo modeling results confirm the effectiveness of the proposed approach.