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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

We study the influence of a bandwidth parameter in inference with conditional estimating equations. In that aim, we propose a new class of smooth minimum distance estimators and we develop a theory that focuses on uniformity in bandwidth. We establish a vn-asymptotic representation of our estimator as a process indexed by a bandwidth that can vary within a wide range including bandwidths independent of the sample size. We develop an efficient version of our estimator. We also study its behavior in misspecified models. 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," TSE Working Papers 13-404, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:27219
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    Cited by:

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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.
    5. Raymond Kan & Cesare Robotti, 0. "Comment on: Pseudo-True SDFs in Conditional Asset Pricing Models," Journal of Financial Econometrics, Oxford University Press, vol. 18(4), pages 729-735.
    6. Xiaolin Sun, 2022. "Estimation of Heterogeneous Treatment Effects Using a Conditional Moment Based Approach," Papers 2210.15829, arXiv.org, revised Oct 2024.
    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.
    22. Hristache, Marian & Patilea, Valentin, 2021. "Equivalent models for observables under the assumption of missing at random," Econometrics and Statistics, Elsevier, vol. 20(C), pages 153-165.
    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:

    • 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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