Wild bootstrap inference for penalized quantile regression for longitudinal data

Carlos Lamarche, Thomas Parker

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish
Pages (from-to)1799-1826
Number of pages28
JournalJournal of Econometrics
Issue number2
StatePublished - Aug 2023

Bibliographical note

Publisher Copyright:
© 2023 Elsevier B.V.


  • Bootstrap inference
  • Panel data
  • Penalized estimator
  • Quantile regression

ASJC Scopus subject areas

  • Applied Mathematics
  • Economics and Econometrics


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