Quantile regression estimation of partially linear additive models

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Abstract

In this paper, we consider the estimation of partially linear additive quantile regression models where the conditional quantile function comprises a linear parametric component and a nonparametric additive component. We propose a two-step estimation approach: in the first step, we approximate the conditional quantile function using a series estimation method. In the second step, the nonparametric additive component is recovered using either a local polynomial estimator or a weighted Nadaraya-Watson estimator. Both consistency and asymptotic normality of the proposed estimators are established. Particularly, we show that the first-stage estimator for the finite-dimensional parameters attains the semiparametric efficiency bound under homoskedasticity, and that the second-stage estimators for the nonparametric additive component have an oracle efficiency property. Monte Carlo experiments are conducted to assess the finite sample performance of the proposed estimators. An application to a real data set is also illustrated.

Original languageEnglish
Pages (from-to)509-536
Number of pages28
JournalJournal of Nonparametric Statistics
Volume26
Issue number3
DOIs
Publication statusPublished - 2014 Jul

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Keywords

  • local polynomial estimation
  • partially linear additive model
  • quantile regression
  • series estimation method
  • weighted Nadaraya-Watson estimation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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