Bahadur efficiencies of the Epps--Pulley test for normality

TL;DR

This paper evaluates the Bahadur efficiencies of the Epps--Pulley test for normality, demonstrating its competitive performance and efficiency over alternatives across various close-to-normal distributions.

Contribution

It provides approximate Bahadur efficiencies for the Epps--Pulley test, extending previous analyses and highlighting its superior performance with certain tuning parameters.

Findings

Epps--Pulley test outperforms competitors for specific tuning parameters.

The test maintains high efficiency across multiple close alternatives to normality.

It is a genuine affine invariant and universally consistent test in any dimension.

Abstract

The test for normality suggested by Epps and Pulley (1983) is a serious competitor to tests based on the empirical distribution function. In contrast to the latter procedures, it has been generalized to obtain a genuine affine invariant and universally consistent test for normality in any dimension. We obtain approximate Bahadur efficiencies for the test of Epps and Pulley, thus complementing recent results of Milo\v{s}evi\'c et al. (2021). For certain values of a tuning parameter that is inherent in the Epps--Pulley test, this test outperforms each of its competitors considered in Milo\v{s}evi\'c et al. (2021), over the whole range of six close alternatives to normality.