On minimum Hellinger distance estimation

Efficiency and robustness are two fundamental concepts in parametric estimation problems. It was long thought that there was an inherent contradiction between the aims of achieving robustness and efficiency; that is, a robust estimator could not be efficient and vice versa. It is now known that the minimum Hellinger distance approached introduced by Beran [R. Beran, Annals of Statistics 1977;5:445–463] is one way of reconciling the conflicting concepts of efficiency and robustness. For parametric models, it has been shown that minimum Hellinger estimators achieve efficiency at the model density and simultaneously have excellent robustness properties. In this article, we examine the application of this approach in two semiparametric models. In particular, we consider a two‐component mixture model and a two‐sample semiparametric model. In each case, we investigate minimum Hellinger distance estimators of finite‐dimensional Euclidean parameters of particular interest and study their basic asymptotic properties. Small sample properties of the proposed estimators are examined using a Monte Carlo study. The results can be extended to semiparametric models of general form as well. The Canadian Journal of Statistics 37: 514–533; 2009 © 2009 Statistical Society of Canada