Local linear quantile regression

Yu, Keming and Jones, M. C. (1998). Local linear quantile regression. Journal of the American Statistical Association, 93(441) pp. 228–237.

URL: http://www.jstor.org/stable/2669619

Abstract

In this article we study nonparametric regression quantile estimation by kernel weighted local linear fitting. Two such estimators are considered. One is based on localizing the characterization of a regression quantile as the minimizer of E{ρ_p (Y - a)|X = x}, where ρ_p is the appropriate "check" function. The other follows by inverting a local linear conditional distribution estimator and involves two smoothing parameters, rather than one. Our aim is to present fully operational versions of both approaches and to show that each works quite well; although either might be used in practice, we have a particular preference for the second. Our automatic smoothing parameter selection method is novel; the main regression quantile smoothing parameters are chosen by rule-of-thumb adaptations of state-of-the-art methods for smoothing parameter selection for regression mean estimation. The techniques are illustrated by application to two datasets and compared in simulations.

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About

• Item ORO ID
• 24037
• Item Type
• Journal Item
• ISSN
• 1537-274X
• Keywords
• bandwidth selection; conditional quantile; kernel estimator; local linear regression; reference chart; rule of thumb
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 1998 American Statistical Association
• Depositing User
• Sarah Frain