An asymptotic theory for model selection inference in general semiparametric problems |
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Authors: | Claeskens Gerda; Carroll Raymond J |
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Institution: | Operations Research & Business Statistics and University Center for Statistics, Katholieke Universiteit Leuven, Naamsestraat 69, B-3000 Leuven, Belgium |
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Abstract: | Hjort & Claeskens (2003) developed an asymptotic theoryfor model selection, model averaging and subsequent inferenceusing likelihood methods in parametric models, along with associatedconfidence statements. In this article, we consider a semiparametricversion of this problem, wherein the likelihood depends on parametersand an unknown function, and model selection/averaging is tobe applied to the parametric parts of the model. We show thatall the results of Hjort & Claeskens hold in the semiparametriccontext, if the Fisher information matrix for parametric modelsis replaced by the semiparametric information bound for semiparametricmodels, and if maximum likelihood estimators for parametricmodels are replaced by semiparametric efficient profile estimators.Our methods of proof employ Le Cam's contiguity lemmas, leadingto transparent results. The results also describe the behaviourof semiparametric model estimators when the parametric componentis misspecified, and also have implications for pointwise-consistentmodel selectors. |
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Keywords: | Akaike information criterion Bayes information criterion Efficient semiparametric estimation Frequentist model averaging Model averaging Model selection Profile likelihood Semiparametric model |
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