A Note on the Relation Between Modified Profile Likelihood and the Cox-Reid Adjusted Profile Likelihood
研究了Cox-Reid调整剖面似然与修正剖面似然在参数非正交情况下的等价性，给出了若干实例，并推导了在复合变换模型中两者等价的充要条件。
An adjustment to the profile likelihood proposed by Cox & Reid (1987) when the parameters are orthogonal is shown to agree with modified profile likelihood in a number of instances in which the parameters are not orthogonal. Several examples of the phenomenon are given. In the case 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 Lebesgue measure is right-invariant. Necessary and sufficient conditions for equivalence in the moderate-deviation sense of modified profile likelihood and the Cox-Reid adjusted profile likelihood are derived.