Local Polynomial Quantile Regression With Parametric Features

• 成果类型: Article
• 署名作者: El Ghouch, Anouar; Genton, Marc G.
• 署名单位: University of Geneva; Texas A&M University System; Texas A&M University College Station
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2009.tm08400
• 发表日期: 2009
• 页码: 1416-1429
• 关键词: cross-validation; least-squares; estimators; algorithm

摘要

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 a-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.