In this dissertation we propose an empirical likelihood ratio (ELR) test to conductnon-nested model selection. It allows for heteroscedasticity and works for any twosupervised statistical learning methods under mild conditions. We establish asymptoticproperties for the ELR test used for model selection between two linear models,between a functional coecient model and a non-parametric regression model, and betweentwo general supervised statistical learning methods. Simulations demonstrategood nite sample performance of our model selection procedure. A real exampleillustrates the use of our methodology.
