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Application of Likelihood Methods to Models Involving Large Numbers of Parameters

John D. Kalbfleisch and D. A. Sprott
Journal of the Royal Statistical Society. Series B (Methodological)
Vol. 32, No. 2 (1970), pp. 175-208
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/2984524
Page Count: 34
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Application of Likelihood Methods to Models Involving Large Numbers of Parameters
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Abstract

Likelihood methods of dealing with some multiparameter problems are introduced and exemplified. Specifically, methods of eliminating nuisance parameters from the likelihood function so that inferences can be made about the parameters of interest are considered. In this regard integrated likelihoods, maximum relative likelihoods, conditional likelihoods, marginal likelihoods and second-order likelihoods are introduced and their uses illustrated in examples. Marginal and conditional likelihoods are dependent upon factorings of the likelihood function. They are applied to the linear functional relationship and to related models and are found to give intuitively appealing results. These methods indicate that in many situations commonly encountered objective methods of eliminating unwanted parameters from the likelihood function can be adopted. This gives an alternative method of interpreting multiparameter likelihoods to that offered by the Bayesian approach.

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