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Abstract:
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We investigate estimation problem of parameters in a two-sample semiparametric model, where the log ratio of the two underlying density functions is of a regression form. This model has wide applications in the logistic discriminant analysis, case-control studies, and receiver operating characteristic curves analysis. 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 the regression parameters. 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.
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