Non-Parametric Goodness-of-Fit Tests Using Tsallis Entropy Measures

TL;DR

This paper introduces new non-parametric goodness-of-fit tests based on Tsallis entropy, focusing on multivariate generalized Gaussian distributions, with improved parameter estimation methods for heavy-tailed and non-Gaussian data.

Contribution

It develops entropy-based tests using Tsallis entropy and proposes an iterative shape parameter estimation method, extending entropy estimation techniques for better accuracy.

Findings

Tests demonstrate good convergence properties

Enhanced estimation accuracy for heavy-tailed distributions

Applicable to machine learning and signal processing

Abstract

In this paper, we investigate new procedures for statistical testing based on Tsallis entropy, a parametric generalization of Shannon entropy. Focusing on multivariate generalized Gaussian and $q$-Gaussian distributions, we develop entropy-based goodness-of-fit tests based on maximum entropy formulations and nearest neighbour entropy estimators. Furthermore, we propose a novel iterative approach for estimating the shape parameters of the distributions, which is crucial for practical inference. This method extends entropy estimation techniques beyond traditional approaches, improving precision in heavy-tailed and non-Gaussian contexts. The numerical experiments are demonstrative of the statistical properties and convergence behaviour of the proposed tests. These findings are important for disciplines that require robust distributional tests, such as machine learning, signal processing, and information theory.