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September, 1988 Differential Geometry, Profile Likelihood, $L$-Sufficiency and Composite Transformation Models
O. E. Barndorff-Nielsen, P. E. Jupp
Ann. Statist. 16(3): 1009-1043 (September, 1988). DOI: 10.1214/aos/1176350946


Let $\Omega$ denote the parameter space of a statistical model and let $\mathscr{K}$ be the domain of variation of the parameter of interest. Various differential-geometric structures on $\Omega$ are considered, including the expected information metric and the $\alpha$-connections studied by Chentsov and Amari, as well as the observed information metric and the observed $\alpha$-connections introduced by Barndorff-Nielsen. Under certain conditions these geometric objects on $\Omega$ can be transferred in a canonical purely differential-geometric way to $\mathscr{K}$. The transferred objects are related to structures on $\mathscr{K}$ obtained from derivatives of pseudolikelihood functions such as the profile likelihood, the modified profile likelihood and the marginal likelihood based on an $L$-sufficient statistic (cf. Remon) when such a statistic exists. For composite transformation models it is shown that the modified profile likelihood is very close to the Laplace approximation to a certain integral representation of the marginal likelihood.


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O. E. Barndorff-Nielsen. P. E. Jupp. "Differential Geometry, Profile Likelihood, $L$-Sufficiency and Composite Transformation Models." Ann. Statist. 16 (3) 1009 - 1043, September, 1988.


Published: September, 1988
First available in Project Euclid: 12 April 2007

zbMATH: 0702.62032
MathSciNet: MR959187
Digital Object Identifier: 10.1214/aos/1176350946

Primary: 62F99
Secondary: 62B05

Rights: Copyright © 1988 Institute of Mathematical Statistics


Vol.16 • No. 3 • September, 1988
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