A test for normality and independence based on characteristic function
Statistics Theory
2023-05-30 v1 Methodology
Statistics Theory
Abstract
In this article we prove a generalization of the Ejsmont characterization of the multivariate normal distribution. Based on it, we propose a new test for independence and normality. The test uses an integral of the squared modulus of the difference between the product of empirical characteristic functions and some constant. Special attention is given to the case of testing univariate normality in which we derive the test statistic explicitly in terms of Bessel function, and the case of testing bivariate normality and independence. The tests show quality performance in comparison to some popular powerful competitors.
Cite
@article{arxiv.2107.04845,
title = {A test for normality and independence based on characteristic function},
author = {Wiktor Ejsmont and Bojana Milošević and Marko Obradović},
journal= {arXiv preprint arXiv:2107.04845},
year = {2023}
}