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An asymptotic theory for model selection inference in general semiparametric problems

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  • Gerda Claeskens
  • Raymond J. Carroll
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    Abstract

    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. Copyright 2007, Oxford University Press.

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    Bibliographic Info

    Article provided by Biometrika Trust in its journal Biometrika.

    Volume (Year): 94 (2007)
    Issue (Month): 2 ()
    Pages: 249-265

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    Handle: RePEc:oup:biomet:v:94:y:2007:i:2:p:249-265

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    Cited by:
    1. Liu, Chu-An, 2013. "Distribution Theory of the Least Squares Averaging Estimator," MPRA Paper 54201, University Library of Munich, Germany.
    2. Wei, Jiawei & Carroll, Raymond J. & Maity, Arnab, 2011. "Testing for constant nonparametric effects in general semiparametric regression models with interactions," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 717-723, July.
    3. Liu, Chu-An & Kuo, Biing-Shen, 2014. "Model Averaging in Predictive Regressions," MPRA Paper 54198, University Library of Munich, Germany.
    4. Maity, Arnab, 2008. "Efficient estimation of population quantiles in general semiparametric regression models," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2744-2750, November.
    5. Liu, Lian, 2007. "Estimation of generalized partially linear models with measurement error using sufficiency scores," Statistics & Probability Letters, Elsevier, vol. 77(15), pages 1580-1588, September.
    6. Toru Kitagawa & Chris Muris, 2013. "Covariate selection and model averaging in semiparametric estimation of treatment effects," CeMMAP working papers CWP61/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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