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Extremes of two-step regression quantiles

Jan Picek and Jan Dienstbier

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The article deals with estimators of extreme value index based on two-step regression quantiles in the linear regression model. Two-step regression quantiles can be seen as a possible generalization of the quantile idea and as an alternative to regression quantiles. We derive the approximation of the tail quantile function of errors. Following Drees (1998) we consider a class of smooth functionals of the tail quantile function as a tool for the construction of estimators in the linear regression context. Pickands, maximum likelihood and probability weighted moments estimators are illustrated on simulated data.

Chapter information

J. Antoch, M. Hušková and P.K. Sen, eds., Nonparametrics and Robustness in Modern Statistical Inference and Time Series Analysis: A Festschrift in honor of Professor Jana Jurečková (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2010), 204-214

First available in Project Euclid: 29 November 2010

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Mathematical Reviews number (MathSciNet)

Primary: 62G30: Order statistics; empirical distribution functions 62G32: Statistics of extreme values; tail inference
Secondary: 62J05: Linear regression

two-step regression quantile R-estimator extreme value index tail function

Copyright © 2010, Institute of Mathematical Statistics


Picek, Jan; Dienstbier, Jan. Extremes of two-step regression quantiles. Nonparametrics and Robustness in Modern Statistical Inference and Time Series Analysis: A Festschrift in honor of Professor Jana Jurečková, 204--214, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2010. doi:10.1214/10-IMSCOLL720.

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