Local polynomial quantile regression with parametric features

Anouar El Ghouch, Marc Genton

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

We propose a new approach to conditional quantile function estimation that combines both parametric and nonparametric techniques. At each design point, a global, possibly incorrect, pilot parametric model is locally adjusted through a kernel smoothing fit. The resulting quantile regression estimator behaves like a parametric estimator when the latter is correct and converges to the nonparametric solution as the parametric start deviates from the true underlying model. We give a Bahadur-type representation of the proposed estimator from which consistency and asymptotic normality are derived under an α-mixing assumption. We also propose a practical bandwidth selector based on the plug-in principle and discuss the numerical implementation of the new estimator. Finally, we investigate the performance of the proposed method via simulations and illustrate the methodology with a data example.

Original languageEnglish (US)
Pages (from-to)1416-1429
Number of pages14
JournalJournal of the American Statistical Association
Volume104
Issue number488
DOIs
StatePublished - Dec 1 2009

Keywords

  • Bias reduction
  • Local polynomial smoothing
  • Model misspecification
  • Robustness
  • Strong mixing sequence

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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