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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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    References listed on IDEAS

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    Cited by:

    1. repec:eee:jmvana:v:158:y:2017:i:c:p:47-59 is not listed on IDEAS
    2. Kotchoni, Rachidi, 2014. "The indirect continuous-GMM estimation," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 464-488.
    3. Antoine, Bertille & Lavergne, Pascal, 2014. "Conditional moment models under semi-strong identification," Journal of Econometrics, Elsevier, vol. 182(1), pages 59-69.
    4. Sueishi, Naoya, 2016. "A simple derivation of the efficiency bound for conditional moment restriction models," Economics Letters, Elsevier, vol. 138(C), pages 57-59.
    5. Vladimir Spokoiny & Mayya Zhilova, 2014. "Bootstrap confidence sets under model misspecification," SFB 649 Discussion Papers SFB649DP2014-067, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. Nguimkeu, Pierre, 2014. "A structural econometric analysis of the informal sector heterogeneity," Journal of Development Economics, Elsevier, vol. 107(C), pages 175-191.

    More about this item

    Keywords

    Semiparametric Estimation; Conditional Estimating Equations; Smoothing Methods; Asymptotic Efficiency; Hypothesis Testing; Bootstrap;

    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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