The performance of univariate goodness-of-fit tests for normality based on the empirical characteristic function in large samples

TL;DR

This paper compares the effectiveness of univariate goodness-of-fit tests for normality, showing that a simple test based on the empirical characteristic function outperforms more complex tests in large samples.

Contribution

It introduces and evaluates a simple normality test based on the empirical characteristic function, demonstrating its superior performance in large samples.

Findings

The simple empirical characteristic function test outperforms complex tests in large samples.

The Epps-Pulley and other frequentist tests are less effective in large samples.

The study provides a comparative analysis of normality tests based on empirical characteristic functions.

Abstract

An empirical power comparison is made between two tests based on the empirical characteristic function and some of the best performing tests for normality. A simple normality test based on the empirical characteristic function calculated in a single point is shown to outperform the more complicated Epps-Pulley test and the frequentist tests included in the study in large samples.