Statistical tests based on Renyi entropy estimation

TL;DR

This paper introduces goodness-of-fit tests for specific multivariate distributions using Renyi entropy estimators based on nearest neighbor distances, with proven consistency and analysis of their convergence and distribution.

Contribution

It presents new goodness-of-fit statistics for multivariate Student and Pearson type II distributions based on Renyi entropy and establishes their theoretical properties.

Findings

Statistics are L2-consistent.

Monte Carlo methods analyze convergence and distribution.

Applicable to multivariate distributions.

Abstract

Entropy and its various generalizations are important in many fields, including mathematical statistics, communication theory, physics and computer science, for characterizing the amount of information associated with a probability distribution. In this paper we propose goodness-of-fit statistics for the multivariate Student and multivariate Pearson type II distributions, based on the maximum entropy principle and a class of estimators for Renyi entropy based on nearest neighbour distances. We prove the L2-consistency of these statistics using results on the subadditivity of Euclidean functionals on nearest neighbour graphs, and investigate their rate of convergence and asymptotic distribution using Monte Carlo methods.