On the corrections to the likelihood ratio statistics

Abstract

Hayakawa's (1977) null asymptotic expansion of the likelihood ratio criterion for testing a composite null hypothesis against a composite alternative hypothesis appears to be in conflict with Lawley (1956) if and only if a certain coefficient is nonzero. It is shown that this coefficient vanishes for all regular problems. Correction factors are derived for generalized linear models when the scale factor is assumed unknown. The present paper generalizes also some results by Cordeiro (1983).