Testing Goodness-of-Fit via Rate Distortion

TL;DR

This paper introduces a novel goodness-of-fit testing framework based on rate distortion theory, which involves compressing data and measuring divergence to assess fit, applicable under broad conditions.

Contribution

It proposes a new testing approach leveraging rate distortion techniques, extending the applicability of goodness-of-fit tests beyond traditional methods.

Findings

The approach can be applied under very general conditions.

Initial special cases show promising results.

The method links data compression with statistical testing.

Abstract

A framework is developed using techniques from rate distortion theory in statistical testing. The idea is first to do optimal compression according to a certain distortion function and then use information divergence from the compressed empirical distribution to the compressed null hypothesis as statistic. Only very special cases have been studied in more detail, but they indicate that the approach can be used under very general conditions.