Bahadur efficiency of EDF based normality tests when parameters are estimated

TL;DR

This paper evaluates the efficiency of empirical distribution function-based normality tests with estimated parameters, providing asymptotic properties and efficiency benchmarks for close alternatives.

Contribution

It revisits well-known EDF-based normality tests, derives new asymptotic results, and calculates approximate Bahadur slopes and efficiencies for close alternatives.

Findings

Approximate Bahadur slopes for EDF-based tests and likelihood ratio test.

Local approximate efficiencies for various close alternatives.

Provides benchmarks for evaluating normality tests.

Abstract

In this paper some well-known tests based on empirical distribution functions (EDF) with estimated parameters for testing composite normality hypothesis are revisited, and some new results on asymptotic properties are provided. In particular, the approximate Bahadur slopes are obtained -- in the case of close alternatives -- for the EDF-based tests as well as the likelihood ratio test. The local approximate efficiencies are calculated for several close alternatives. The obtained results could serve as a benchmark for evaluation of the quality of recent and future normality tests.