Heteroscedasticity diagnostics of error variance is essential before performing some statistical inference work. This paper is concerned with the statistical diagnostics for the varying coefficient partially nonlinear model. We propose a novel diagnostic approach for heteroscedasticity of error variance in the model by combining it with the empirical likelihood method. Under some mild conditions, the nonparametric version of the Wilks theorem is obtained. Furthermore, simulation studies and a real data analysis are implemented to evaluate the performances of our proposed approaches.

This paper explored the effective empirical likelihood inferences for partially nonlinear models. By combining the modal regression method with orthogonal projection technology, a modal empirical likelihood-based estimation procedure was proposed. The proposed empirical likelihood approach retained Wilk's theorem under mild conditions, and the confidence regions of model coefficients were constructed. Nonparametric and parametric components of the estimators were independent. Simulation results demonstrated that it is more robust and effective than the existing methods.