Estimation and variable selection for proportional response data with partially linear single-index models

Empirical researchers are often faced with the need to model proportional data in many fields such as econometrics, finance and biostatistics. In this paper, we study a robust and flexible modeling of proportional data using quasi-likelihood method with partially linear single-index structure. Bias-corrected estimating equations are developed to fit the model with the nonparametric function being approximated by polynomial splines. The theoretical properties of the estimators are established. In addition, we apply the regularization approach to simultaneously select significant variables and estimate unknown parameters, and the resulting penalized estimators are shown to have the oracle property. Extensive simulation studies and an empirical example are used to illustrate the usefulness of the newly proposed methods.