On M-estimators and normal quantiles

This paper explores a class of robust estimators of normal quantiles filling the gap between maximum likelihood estimators and empirical quantiles. Our estimators are linear combinations of M-estimators. Their asymptotic variances can be arbitrarily close to variances of the maximum likelihood estimators. Compared with empirical quantiles, the new estimators offer considerable reduction of variance at near normal probability distributions.16 page(s