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 X1,…,XnX1,…,Xn be a sample from a population with distribution function GG and density function gg. Independent of the XiXi’s, let Z1,…,ZmZ1,…,Zm be another random sample with distribution function HH and density function h(x)=exp[α+r(x)β]g(x)h(x)=exp[α+r(x)β]g(x), where αα and ββ are unknown parameters of interest and gg 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 αα and ββ. 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.