# A plug-in bandwidth selector for nonparametric quantile regression

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## Abstract

In the framework of quantile regression, local linear smoothing techniques have been studied by several authors, particularly by Yu and Jones (J Am Stat Assoc 93:228–237, 1998). The problem of bandwidth selection was addressed in the literature by the usual approaches, such as cross-validation or plug-in methods. Most of the plug-in methods rely on restrictive assumptions on the quantile regression model in relation to the mean regression, or on parametric assumptions. Here we present a plug-in bandwidth selector for nonparametric quantile regression that is defined from a completely nonparametric approach. To this end, the curvature of the quantile regression function and the integrated squared sparsity (inverse of the conditional density) are both nonparametrically estimated. The new bandwidth selector is shown to work well in different simulated scenarios, particularly when the conditions commonly assumed in the literature are not satisfied. A real data application is also given.

## Keywords

Quantile regression Bandwidth Nonparametric regression## Mathematics Subject Classification

62G08## Notes

### Acknowledgements

The authors gratefully acknowledge the support of Projects MTM2013–41383–P (Spanish Ministry of Economy, Industry and Competitiveness) and MTM2016–76969–P (Spanish State Research Agency, AEI), both co-funded by the European Regional Development Fund (ERDF). Support from the IAP network StUDyS, from Belgian Science Policy, is also acknowledged. Work of M. Conde-Amboage has been supported by FPU grant AP2012-5047 from the Spanish Ministry of Education. We are grateful to two anonymous referees for their constructive comments, which helped to improve the paper.

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