Likelihood Inferences on Semiparametric Odds Ratio Model

The semiparametric odds ratio model is particularly useful for analyzing biased sampling designs. However, statistical inference of the model has not been systematically studied when more than one nonparametric component is involved in the model.

In this article, we study the maximum semiparametric likelihood approach to estimation and inference of the semiparametric odds ratio model. We show that the maximum semiparametric likelihood estimator of the odds ratio parameter is consistent and asymptotically normally distributed. We also establish statistical inference under a misspecified semiparametric odds ratio model, which is important when handling weak identifiability in conditionally specified models under biased sampling designs.