Local Quantile Regression

SFB 649 Discussion Paper 2011-005

32 Pages Posted: 9 Jan 2017

See all articles by Wolfgang K. Härdle

Wolfgang K. Härdle

Humboldt University of Berlin - Institute for Statistics and Econometrics; Xiamen University - Wang Yanan Institute for Studies in Economics (WISE); Charles University; Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

V. Spokoiny

Weierstras Institute for Applied Analysis and Stochastics (WIAS)

Weining Wang

Humboldt University of Berlin

Date Written: December 13, 2010

Abstract

Conditional quantile curves provide a comprehensive picture of a response contingent on explanatory variables. Quantile regression is a technique to estimate such curves. In a flexible modeling framework, a specific form of the quantile is not a priori fixed. Indeed, the majority of applications do not per se require specific functional forms. This motivates a local parametric rather than a global fixed model fitting approach. A nonparametric smoothing estimate of the conditional quantile curve requires to consider a balance between local curvature and variance. In this paper, we analyze a method based on a local model selection technique that provides an adaptive estimate. Theoretical properties on mimicking the oracle choice are offered and applications to stock market and weather analysis are presented.

Keywords: Conditional Quantiles, Semiparametric and Nonparametric Methods, Asymmetric Laplace Distribution, Exponential Risk Bounds, Adaptive Bandwidth Selection

JEL Classification: C00, C14, J01, J31

Suggested Citation

Härdle, Wolfgang K. and Spokoiny, Vladimir and Wang, Weining, Local Quantile Regression (December 13, 2010). SFB 649 Discussion Paper 2011-005. Available at SSRN: https://ssrn.com/abstract=2894253 or http://dx.doi.org/10.2139/ssrn.2894253

Wolfgang K. Härdle (Contact Author)

Humboldt University of Berlin - Institute for Statistics and Econometrics ( email )

Unter den Linden 6
Berlin, D-10099
Germany

Xiamen University - Wang Yanan Institute for Studies in Economics (WISE) ( email )

A 307, Economics Building
Xiamen, Fujian 10246
China

Charles University ( email )

Celetná 13
Dept Math Physics
Praha 1, 116 36
Czech Republic

Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Unter den Linden 6
Berlin, D-10099
Germany

Vladimir Spokoiny

Weierstras Institute for Applied Analysis and Stochastics (WIAS) ( email )

Mohrenstr. 39
Berlin, 10117
Germany

Weining Wang

Humboldt University of Berlin ( email )

Unter den Linden 6
Berlin, AK Berlin 10099
Germany

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