An asymptotic theory for model selection inference in general semiparametric problems

Hjort & Claeskens (2003) developed an asymptotic theory for model selection, model averaging and subsequent inference using likelihood methods in parametric models, along with associated confidence statements. In this article, we consider a semiparametric version of this problem, wherein the lik...

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Bibliographic Details
Published in:Biometrika 2007-06, Vol.94 (2), p.249-265
Main Authors: Claeskens, Gerda, Carroll, Raymond J.
Format: Article
Language:English
Subjects:
Akaike information criterion
Applications
Asymptotic theory
Bayes information criterion
Bayesian analysis
Biology, psychology, social sciences
Confidence interval
Consistent estimators
Efficient semiparametric estimation
Estimating techniques
Estimators
Exact sciences and technology
Fisher information
Frequentist model averaging
General topics
Generalized linear models
Inference
Logic and foundations
Mathematical logic, foundations, set theory
Mathematical models
Mathematics
Model averaging
Model selection
Model theory
Musical intervals
Parametric inference
Parametric models
Partial derivatives
Probability and statistics
Profile likelihood
Sciences and techniques of general use
Semiparametric model
Semiparametric modeling
Statistics
Studies
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Summary:Hjort & Claeskens (2003) developed an asymptotic theory for model selection, model averaging and subsequent inference using likelihood methods in parametric models, along with associated confidence statements. In this article, we consider a semiparametric version of this problem, wherein the likelihood depends on parameters and an unknown function, and model selection/averaging is to be applied to the parametric parts of the model. We show that all the results of Hjort & Claeskens hold in the semiparametric context, if the Fisher information matrix for parametric models is replaced by the semiparametric information bound for semiparametric models, and if maximum likelihood estimators for parametric models are replaced by semiparametric efficient profile estimators. Our methods of proof employ Le Cam's contiguity lemmas, leading to transparent results. The results also describe the behaviour of semiparametric model estimators when the parametric component is misspecified, and also have implications for pointwise-consistent model selectors.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/asm034