Existing work on penalized quantile regression for longitudinal data has been focused almost exclusively on point estimation. In this work, we investigate statistical inference. We first show that the pairs bootstrap that samples cross-sectional units with replacement does not approximate well the limiting distribution of the penalized estimator. We then propose a wild residual bootstrap procedure and show that it is asymptotically valid for approximating the distribution of the penalized estimator. The  new method is easy to implement and uses weight distributions that are standard in the literature. Simulation studies are carried out to investigate the small sample behavior of the proposed approach in comparison with existing procedures. Finally, we illustrate the new approach using U.S. Census data to estimate a high-dimensional model that includes more than eighty thousand parameters.
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.
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Existing work on
The existing theory of
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been focused almost exclusively
focused primarily
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first show that the pairs bootstrap that samples cross-sectional units with replacement does not approximate well the limiting distribution of the penalized estimator. We then
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model puts no restrictions on individual effects, and the estimator achieves consistency by letting the shrinkage decay in importance asymptotically. The
R
uses weight distributions that are standard in the literature. Simulation studies are carried out to investigate the
simulation studies show that it has accurate
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of the proposed approach
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high-dimensional