Open Access
Translator Disclaimer
December, 1986 Invariants and Likelihood Ratio Statistics
P. McCullagh, D. R. Cox
Ann. Statist. 14(4): 1419-1430 (December, 1986). DOI: 10.1214/aos/1176350167


Because the likelihood ratio statistic is invariant under reparameterization, it is possible to make a large-sample expansion of the statistic itself and of its expectation in terms of invariants. In particular, the Bartlett adjustment factor can be expressed in terms of invariant combinations of cumulants of the first two log-likelihood derivatives. Such expansions are given, first for a scalar parameter and then for vector parameters. Geometrical interpretation is given where possible and some special cases discussed.


Download Citation

P. McCullagh. D. R. Cox. "Invariants and Likelihood Ratio Statistics." Ann. Statist. 14 (4) 1419 - 1430, December, 1986.


Published: December, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0615.62041
MathSciNet: MR868309
Digital Object Identifier: 10.1214/aos/1176350167

Primary: 62F99
Secondary: 62E20

Keywords: asymptotic expansion , Bartlett factor , cumulant tensor , curvature , geometry , intrinsic , invariant , likelihood ratio statistic , tensor derivative

Rights: Copyright © 1986 Institute of Mathematical Statistics


Vol.14 • No. 4 • December, 1986
Back to Top