Oe. Barndorffnielsen et P. Mccullagh, A NOTE ON THE RELATION BETWEEN MODIFIED PROFILE LIKELIHOOD AND THE COX-REID ADJUSTED PROFILE LIKELIHOOD, Biometrika, 80(2), 1993, pp. 321-328
Citations number
8
Categorie Soggetti
Mathematical Methods, Biology & Medicine","Statistic & Probability
An adjustment to the profile likelihood proposed by Cox & Reid (1987)
when the parameters are orthogonal is shown to agree with modified pro
file likelihood in a number of instances in which the parameters are n
ot orthogonal. Several examples of the phenomenon are given. In the ca
se of composite transformation models with invariant parameter as the
parameter of interest, it is shown that the Cox-Reid adjustment agrees
with modified profile likelihood in a large-deviation sense if Lebesg
ue measure is right-invariant. Necessary and sufficient conditions for
equivalence in the moderate-deviation sense of modified profile likel
ihood and the Cox-Reid adjusted profile likelihood are derived.