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An asymptotic theory for model selection inference in general semiparametric problems

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  • Gerda Claeskens
  • Raymond J. Carroll

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.

Suggested Citation

  • Gerda Claeskens & Raymond J. Carroll, 2007. "An asymptotic theory for model selection inference in general semiparametric problems," Biometrika, Biometrika Trust, vol. 94(2), pages 249-265.
  • Handle: RePEc:oup:biomet:v:94:y:2007:i:2:p:249-265
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    File URL: http://hdl.handle.net/10.1093/biomet/asm034
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    Citations

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    Cited by:

    1. 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.
    2. Toru Kitagawa & Chris Muris, 2015. "Model averaging in semiparametric estimation of treatment effects," CeMMAP working papers CWP46/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Kitagawa, Toru & Muris, Chris, 2016. "Model averaging in semiparametric estimation of treatment effects," Journal of Econometrics, Elsevier, vol. 193(1), pages 271-289.
    4. Hai Ying Wang & Xinjie Chen & Nancy Flournoy, 2016. "The focused information criterion for varying-coefficient partially linear measurement error models," Statistical Papers, Springer, vol. 57(1), pages 99-113, March.
    5. repec:spr:metrik:v:80:y:2017:i:5:d:10.1007_s00184-017-0616-1 is not listed on IDEAS
    6. Gerda Claeskens, 2012. "Focused estimation and model averaging with penalization methods: an overview," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 66(3), pages 272-287, August.
    7. Liu, Chu-An, 2015. "Distribution theory of the least squares averaging estimator," Journal of Econometrics, Elsevier, vol. 186(1), pages 142-159.
    8. Chu‐An Liu & Biing‐Shen Kuo, 2016. "Model averaging in predictive regressions," Econometrics Journal, Royal Economic Society, vol. 19(2), pages 203-231, June.
    9. Zhang, Qingzhao & Duan, Xiaogang & Ma, Shuangge, 2017. "Focused information criterion and model averaging with generalized rank regression," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 11-19.
    10. 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.
    11. Shou-Yung Yin & Chu-An Liu & Chang-Ching Lin, 2016. "Focused Information Criterion and Model Averaging for Large Panels with a Multifactor Error Structure," IEAS Working Paper : academic research 16-A016, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    12. Ruoyao Shi & Zhipeng Liao, 2018. "An Averaging GMM Estimator Robust to Misspecification," Working Papers 201803, University of California at Riverside, Department of Economics.
    13. Maity, Arnab, 2008. "Efficient estimation of population quantiles in general semiparametric regression models," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2744-2750, November.
    14. 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.
    15. Xu Cheng & Zhipeng Liao & Ruoyao Shi, 2013. "Uniform Asymptotic Risk of Averaging GMM Estimator Robust to Misspecification, Second Version," PIER Working Paper Archive 15-017, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 25 Mar 2015.

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