Cross Validation for Comparing Multiple Density Estimation Procedures

TL;DR

This paper proves that cross validation reliably compares multiple density estimation methods, even in nonparametric settings, by establishing likelihood ratio inequalities, expanding the theoretical understanding of model evaluation techniques.

Contribution

It introduces a new theoretical result showing the consistency of cross validation for comparing density estimators without requiring data domination, extending prior work.

Findings

Cross validation is consistent for density estimation comparison.

No need for test data domination in nonparametric cases.

Complements previous theoretical results by Yang (2005, 2006).

Abstract

We demonstrate the consistency of cross validation for comparing multiple density estimators using simple inequalities on the likelihood ratio. In nonparametric problems, the splitting of data does not require the domination of test data over the training/estimation data, contrary to Shao (1993). The result is complementary to that of Yang (2005) and Yang (2006).