Nonnested model selection based on empirical likelihood

TL;DR

This paper introduces an empirical likelihood ratio test for flexible nonparametric model selection that handles various model relationships, heteroscedasticity, and large datasets, with proven asymptotic properties and practical implementation.

Contribution

It develops a novel empirical likelihood-based test for diverse model comparisons, extending to variable significance testing in large additive models.

Findings

The test performs well in simulations with favorable finite sample properties.

It is applicable to a wide range of models including nested, nonnested, and misspecified.

The method is validated through an empirical application.

Abstract

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.