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Simultaneous estimation of linear conditional quantiles with penalized splines

journal contribution
posted on 05.11.2021, 12:26 authored by Heng Lian, Jie MengJie Meng, Zengyan Fan
We consider smooth estimation of the conditional quantile process in linear models using penalized splines. For linear quantile regression problems, usually separate models are fitted at a finite number of quantile levels and then information from different quantiles is combined in interpreting the results. We propose a smoothing method based on penalized splines that computes the conditional quantiles all at the same time. We consider both fixed-knots and increasing-knots asymptotics of the estimator and show that it converges to a multivariate Gaussian process. Simulations show that smoothing can result in more accurate estimation of the conditional quantiles. The method is further illustrated on a real data set. Empirically (although not theoretically) we observe that the crossing quantile curves problem can often disappear using the smoothed estimator.

History

School

  • Loughborough University London

Published in

Journal of Multivariate Analysis

Volume

141

Pages

1 - 21

Publisher

Elsevier BV

Version

VoR (Version of Record)

Rights holder

© Elsevier

Publisher statement

This paper was accepted for publication in the journal Journal of Multivariate Analysis and the definitive published version is available at https://doi.org/10.1016/j.jmva.2015.06.010.

Publication date

2015-06-24

Copyright date

2015

ISSN

0047-259X

eISSN

1095-7243

Language

en

Depositor

Dr Jie Meng. Deposit date: 4 November 2021

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