Minimum Hellinger distance estimation in a two-sample semiparametric model

We investigate the estimation problem of parameters in a two-sample semiparametric model. Specifically, let X-1, ..., X-n be a sample from a population with distribution function G and density function g. Independent of the X-i's, let Z(1), ..., Z(m) be another random sample with distribution function H and density function h(x) = exp[alpha + r(x)beta]g (x), where alpha and beta are unknown parameters of interest and g is an unknown density. This model has wide applications in logistic discriminant analysis, case-control studies, and analysis of receiver operating characteristic curves. Furthermore, it can be considered as a biased sampling model with weight function depending on unknown parameters. In this paper, we construct minimum Hellinger distance estimators of alpha and beta. The proposed estimators are chosen to minimize the Hellinger distance between a semiparametric model and a nonparametric density estimator. Theoretical properties such as the existence, strong consistency and asymptotic normality are investigated. Robustness of proposed estimators is also examined using a Monte Carlo study. (C) 2010 Elsevier Inc. All rights reserved.