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Wild bootstrap inference for penalized quantile regression for longitudinal data

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  • Lamarche, Carlos
  • Parker, Thomas

Abstract

The existing theory of penalized quantile regression for longitudinal data has focused primarily on point estimation. In this work, we investigate statistical inference. We propose a wild residual bootstrap procedure and show that it is asymptotically valid for approximating the distribution of the penalized estimator. The model puts no restrictions on individual effects, and the estimator achieves consistency by letting the shrinkage decay in importance asymptotically. The new method is easy to implement and simulation studies show that it has accurate small sample behavior in comparison with existing procedures. Finally, we illustrate the new approach using U.S. Census data to estimate a model that includes more than eighty thousand parameters.

Suggested Citation

  • Lamarche, Carlos & Parker, Thomas, 2023. "Wild bootstrap inference for penalized quantile regression for longitudinal data," Journal of Econometrics, Elsevier, vol. 235(2), pages 1799-1826.
    • Handle: RePEc:eee:econom:v:235:y:2023:i:2:p:1799-1826
    DOI: 10.1016/j.jeconom.2022.11.011
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    2. Hartley, Robert Paul & Lamarche, Carlos & Ziliak, James P., 2023. "Bootstrapping quantile correlations with an application for income status across generations," Economics Letters, Elsevier, vol. 228(C).

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    More about this item

    Keywords

    Quantile regression; Panel data; Penalized estimator; Bootstrap inference;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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