Bahadur efficiency for certain goodness--of--fit tests based on the empirical characteristic function

TL;DR

This paper evaluates the Bahadur efficiency of weighted L2--type goodness--of--fit tests based on the empirical characteristic function for normal, exponential, and logistic distributions, providing new efficiency results including multivariate cases.

Contribution

It introduces novel Bahadur efficiency calculations for these tests, especially for the logistic distribution and multivariate normality, guiding practitioners in test selection.

Findings

New efficiency results for BHEP and energy tests for normality

First efficiency computations for goodness--of--fit to the logistic distribution

Efficiency insights for multivariate cases

Abstract

We study the Bahadur efficiency of several weighted L2--type goodness--of--fit tests based on the empirical characteristic function. The methods considered are for normality and exponentiality testing, and for testing goodness--of--fit to the logistic distribution. Our results are helpful in deciding which specific test a potential practitioner should apply. For the celebrated BHEP and energy tests for normality we obtain novel efficiency results, with some of them in the multivariate case, while in the case of the logistic distribution this is the first time that efficiencies are computed for any composite goodness--of--fit test.