Empirical likelihood approach to goodness of fit testing

TL;DR

This paper extends the empirical likelihood method for goodness of fit testing, accommodating growing constraints and nuisance parameters, and develops tests for various distributions and independence in multivariate data.

Contribution

It introduces a generalized empirical likelihood framework that handles increasing constraints and estimated criteria functions, enabling flexible goodness of fit tests.

Findings

Tests are asymptotically distribution free.

Developed goodness of fit tests for univariate distributions.

Created independence tests for bivariate data.

Abstract

Motivated by applications to goodness of fit testing, the empirical likelihood approach is generalized to allow for the number of constraints to grow with the sample size and for the constraints to use estimated criteria functions. The latter is needed to deal with nuisance parameters. The proposed empirical likelihood based goodness of fit tests are asymptotically distribution free. For univariate observations, tests for a specified distribution, for a distribution of parametric form, and for a symmetric distribution are presented. For bivariate observations, tests for independence are developed.