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Sieve M inference on irregular parameters

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  • Chen, Xiaohong
  • Liao, Zhipeng

Abstract

This paper presents sieve inferences on possibly irregular (i.e., slower than root-n estimable) functionals of semi-nonparametric models with i.i.d. data. We provide a simple consistent variance estimator of the plug-in sieve M estimator of a possibly irregular functional, and the asymptotic standard normality of the sieve t statistic. We show that, for hypothesis testing of irregular functionals, the sieve likelihood ratio statistic is asymptotically Chi-square distributed. These results are useful in inference on structural parameters that may have singular semiparametric efficiency bounds. A simulation study and an empirical application of Heckman and Singer (1984) duration model are presented.

Suggested Citation

  • Chen, Xiaohong & Liao, Zhipeng, 2014. "Sieve M inference on irregular parameters," Journal of Econometrics, Elsevier, vol. 182(1), pages 70-86.
    • Handle: RePEc:eee:econom:v:182:y:2014:i:1:p:70-86
    DOI: 10.1016/j.jeconom.2014.04.009
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    9. Nail Kashaev, 2018. "Identification and estimation of multinomial choice models with latent special covariates," Papers 1811.05555, arXiv.org, revised Mar 2022.
    10. Escanciano, Juan Carlos, 2023. "Irregular identification of structural models with nonparametric unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 234(1), pages 106-127.
    11. Ming Li, 2021. "Identification and Estimation in a Time-Varying Endogenous Random Coefficient Panel Data Model," Papers 2110.00982, arXiv.org, revised Nov 2024.
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    14. Laurent Delsol & Ingrid Van Keilegom, 2020. "Semiparametric M-estimation with non-smooth criterion functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(2), pages 577-605, April.

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    More about this item

    Keywords

    Irregular functional; Sieve M estimation; Sieve t statistic; Sieve likelihood ratio; Zero information; Semiparametric duration model;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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