A test for normality and independence based on characteristic function

TL;DR

This paper introduces a new statistical test for normality and independence based on characteristic functions, generalizing previous characterizations and demonstrating strong performance against existing methods.

Contribution

It proposes a novel test leveraging characteristic functions, including explicit formulas for univariate and bivariate cases, improving detection power over traditional tests.

Findings

Test performs well compared to popular competitors

Explicit formulas derived for univariate and bivariate cases

Generalizes Ejsmont's characterization of multivariate normality

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.