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Smooth minimum distance estimation and testing with conditional estimating equations: Uniform in bandwidth theory

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  • Lavergne, Pascal
  • Patilea, Valentin

Abstract

To study the influence of a bandwidth parameter in inference with conditional moments, we propose a new class of estimators and establish an asymptotic representation of our estimator as a process indexed by a bandwidth, which can vary within a wide range including bandwidths independent of the sample size. We study its behavior under misspecification. We also propose an efficient version of our estimator. We develop a procedure based on a distance metric statistic for testing restrictions on parameters as well as a bootstrap technique to account for the bandwidth’s influence. Our new methods are simple to implement, apply to non-smooth problems, and perform well in our simulations.

Suggested Citation

  • Lavergne, Pascal & Patilea, Valentin, 2013. "Smooth minimum distance estimation and testing with conditional estimating equations: Uniform in bandwidth theory," Journal of Econometrics, Elsevier, vol. 177(1), pages 47-59.
    • Handle: RePEc:eee:econom:v:177:y:2013:i:1:p:47-59
    DOI: 10.1016/j.jeconom.2013.05.006
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    3. Antoine, Bertille & Lavergne, Pascal, 2023. "Identification-robust nonparametric inference in a linear IV model," Journal of Econometrics, Elsevier, vol. 235(1), pages 1-24.
    4. Fan, Yanqin & Liu, Ruixuan, 2018. "Partial identification and inference in censored quantile regression," Journal of Econometrics, Elsevier, vol. 206(1), pages 1-38.
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    7. Sueishi, Naoya, 2016. "A simple derivation of the efficiency bound for conditional moment restriction models," Economics Letters, Elsevier, vol. 138(C), pages 57-59.
    8. Kunyang Song & Feiyu Jiang & Ke Zhu, 2024. "Estimation for conditional moment models based on martingale difference divergence," Papers 2404.11092, arXiv.org.
    9. Laurent Davezies & Xavier D'Haultfœuille & Martin Mugnier, 2023. "Fixed‐effects binary choice models with three or more periods," Quantitative Economics, Econometric Society, vol. 14(3), pages 1105-1132, July.
    10. Bianchi, Pascal & Elgui, Kevin & Portier, François, 2023. "Conditional independence testing via weighted partial copulas," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    11. Zdeněk Hlávka & Marie Hušková & Claudia Kirch & Simos G. Meintanis, 2017. "Fourier--type tests involving martingale difference processes," Econometric Reviews, Taylor & Francis Journals, vol. 36(4), pages 468-492, April.
    12. J. S. Allison & M. Hušková & S. G. Meintanis, 2018. "Testing the adequacy of semiparametric transformation models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 70-94, March.
    13. Andrii Babii, 2022. "High-Dimensional Mixed-Frequency IV Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1470-1483, October.
    14. Kotchoni, Rachidi, 2014. "The indirect continuous-GMM estimation," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 464-488.
    15. Bertille Antoine & Xiaolin Sun, 2022. "Partially linear models with endogeneity: a conditional moment-based approach [Efficient estimation of models with conditional moment restrictions containing unknown functions]," The Econometrics Journal, Royal Economic Society, vol. 25(1), pages 256-275.
    16. Li, Weiyu & Patilea, Valentin, 2017. "A new minimum contrast approach for inference in single-index models," Journal of Multivariate Analysis, Elsevier, vol. 158(C), pages 47-59.
    17. Bertille Antoine & Pascal Lavergne, 2020. "Identification-Robust Nonparametric Interference in a Linear IV Model," Discussion Papers dp20-03, Department of Economics, Simon Fraser University.
    18. Nguimkeu, Pierre, 2014. "A structural econometric analysis of the informal sector heterogeneity," Journal of Development Economics, Elsevier, vol. 107(C), pages 175-191.
    19. Jean-Pierre Florens & Elia Lapenta, 2022. "Partly Linear Instrumental Variables Regressions without Smoothing on the Instruments," Papers 2212.11012, arXiv.org, revised Oct 2023.
    20. Spokoiny, Vladimir & Zhilova, Mayya, 2014. "Bootstrap confidence sets under model misspecification," SFB 649 Discussion Papers 2014-067, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    21. Antoine, Bertille & Lavergne, Pascal, 2014. "Conditional moment models under semi-strong identification," Journal of Econometrics, Elsevier, vol. 182(1), pages 59-69.
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    23. Stéphane Goutte & David Guerreiro & Bilel Sanhaji & Sophie Saglio & Julien Chevallier, 2019. "International Financial Markets," Post-Print halshs-02183053, HAL.

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    More about this item

    Keywords

    Semiparametric estimation; Conditional estimating equations; Smoothing methods; Asymptotic efficiency; Hypothesis testing; Bootstrap;
    All these keywords.

    JEL classification:

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

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