Nonparametric estimation of the log odds ratio for sparse data by kernel smoothing

Regression analysis of the odds ratios for sparse data has received a lot of attention. However, existing works are restricted to the parametric case, and a parametric model may be a misspecification, which may lead to biased and inefficient estimators. Little attention is received for nonparametric regression analysis of the odds ratios. Based on kernel smoothing techniques, we propose two simple estimators of the log odds-ratio function for sparse data. Large sample properties of the estimators are derived, and the methods proposed are evaluated through simulation.