  We propose an empirical likelihood ratio test for nonparametric model
selection, where the competing models may be nested, nonnested, overlapping,
misspecified, or correctly specified. It compares the squared prediction errors
of models based on the cross-validation and allows for heteroscedasticity of
the errors of models. We develop its asymptotic distributions for comparing
additive models and varying-coefficient models and extend it to test
significance of variables in additive models with massive data. The method is
applicable to model selection among supervised learning models. To facilitate
implementation of the test, we provide a fast calculation procedure.
Simulations show that the proposed tests work well and have favorable finite
sample performance over some existing approaches. The methodology is validated
on an empirical application.
