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Model Robust Confidence Intervals Using Maximum Likelihood Estimators

Richard M. Royall
International Statistical Review / Revue Internationale de Statistique
Vol. 54, No. 2 (Aug., 1986), pp. 221-226
DOI: 10.2307/1403146
Stable URL: http://www.jstor.org/stable/1403146
Page Count: 6
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Model Robust Confidence Intervals Using Maximum Likelihood Estimators
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Abstract

Standard large-sample confidence intervals about a maximum likelihood estimator θ̂ are two-thirds robust; i.e. when the parametric model is imperfect θ̂ often remains consistent and asymptotically normal. The confidence intervals are invalidated only because the third necessary condition, consistency of the variance estimator, fails. The 'delta method' provides a simple alternative variance estimator which remains consistent under more general conditions and provides robust large-sample confidence intervals. /// Les intervalles de confiance habituels calculés à partir de la théorie des grands échantillons des estimateurs du maximum de vraisemblance sont robustes à deux tiers-lorsque le modèle paramétrique fait défaut, l'estimateur du maximum de vraisemblance θ̂ demeure souvent consistant et asymptotiquement normal. Les intervalles de confiance sont invalidés seulement à cause de l'échec de la troisième condition nécessaire: la consistance de l'estimateur de la variance. La "méthode delta" fournit un estimateur alternatif simple de la variance qui demeure consistant sous des conditions plus générales et qui donne par conséquent des intervalles de confiance robustes.

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