A Note on the Relation Between Modified Profile Likelihood and the Cox-Reid Adjusted Profile Likelihood
Copyright policy )A Note on the Relation Between Modified Profile Likelihood and the Cox-Reid Adjusted Profile Likelihood
Summary: An adjustment to the profile likelihood proposed by \textit{D. R. Cox} and \textit{N. Reid} [J. R. Stat. Soc., Ser. B 49, 1-39 (1987; Zbl 0616.62006)] 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.
- University of Chicago United States
- Aarhus University Denmark
invariant measure, large deviation, Lebesgue measure, orthogonal parameters, moderate deviations, composite transformation models, adjusted profile likelihood, nuisance parameter, invariant parameter, Foundations and philosophical topics in statistics, modified profile likelihood, group transformation model, examples
invariant measure, large deviation, Lebesgue measure, orthogonal parameters, moderate deviations, composite transformation models, adjusted profile likelihood, nuisance parameter, invariant parameter, Foundations and philosophical topics in statistics, modified profile likelihood, group transformation model, examples
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).7 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!