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On Profile Likelihood

S. A. Murphy and A. W. van der Vaart
Journal of the American Statistical Association
Vol. 95, No. 450 (Jun., 2000), pp. 449-465
DOI: 10.2307/2669386
Stable URL: http://www.jstor.org/stable/2669386
Page Count: 17
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On Profile Likelihood
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Abstract

We show that semiparametric profile likelihoods, where the nuisance parameter has been profiled out, behave like ordinary likelihoods in that they have a quadratic expansion. In this expansion the score function and the Fisher information are replaced by the efficient score function and efficient Fisher information. The expansion may be used, among others, to prove the asymptotic normality of the maximum likelihood estimator, to derive the asymptotic chi-squared distribution of the log-likelihood ratio statistic, and to prove the consistency of the observed information as an estimator of the inverse of the asymptotic variance.

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