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Biometrika 1987 74(1):45-58; doi:10.1093/biomet/74.1.45
© 1987 by Biometrika Trust
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Canonical likelihoods: A new likelihood treatment of nuisance parameters

JOHN HINDE and MURRAY AITKIN

Department of Mathematical Statistics and Operational Research, University of Exeter Exeter EX4 4PU, UK.
Centre for Applied Statistics, University of Lancaster Lancaster LA1 4YL, U.K.

A new approach to the likelihood analysis of models with nuisance parameters is proposed, based on a singular value decomposition of the likelihood function, and is applied to several two-parameter models. The invariance of the approach under reparameterization is demonstrated, and the paper concludes with comments on multiparameter models.

Key Words: Canonical • Elimination • Likelihood • Nuisance parameter • Partial likelihood • Singular value decomposition


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