Empirical likelihood based inference for generalized additive partial linear models

Empirical-likelihood based inference for the parameters in generalized additive partial linear models (GAPLM) is investigated. With the use of the polynomial spline smoothing for estimation of nonparametric functions, an estimated empirical likelihood ratio statistic based on the quasi-likelihood equation is proposed. We show that the resulting statistic is asymptotically standard chi-squared distributed and the confidence regions for the parametric components are constructed. Some simulations are conducted to illustrate the proposed methods.