Bartlett-type adjustments for empirical discrepancy test statistics

This paper derives two Bartlett-type adjustments that can be used to obtain higher-order improvements to the distribution of the class of empirical discrepancy test statistics recently introduced by Corcoran (Biometrika 85 (1998) 967) as a generalisation of Owen's (Biometrika 36 (1988) 237) empirical likelihood. The corrections are illustrated in the context of the so-called Cressie–Read goodness-of-fit statistic (Biometrika 85 (1998) 535), and their effectiveness in finite samples is evaluated using simulations.