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

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