Leng, Chenlei and Zhang, Weiping (2014) Smoothing combined estimating equations in quantile regression for longitudinal data. Statistics and Computing, Volume 24 (Number 1). pp. 123-136. doi:10.1007/s11222-012-9358-0

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Abstract

Quantile regression has become a powerful complement to the usual mean regression. A simple approach to use quantile regression in marginal analysis of longitudinal data is to assume working independence. However, this may incur potential efficiency loss. On the other hand, correctly specifying a working correlation in quantile regression can be difficult. We propose a new quantile regression model by combining multiple sets of unbiased estimating equations. This approach can account for correlations between the repeated measurements and produce more efficient estimates. Because the objective function is discrete and non-convex, we propose induced smoothing for fast and accurate computation of the parameter estimates, as well as their asymptotic covariance, using Newton-Raphson iteration. We further develop a robust quantile rank score test for hypothesis testing. We show that the resulting estimate is asymptotically normal and more efficient than the simple estimate using working independence. Extensive simulations and a real data analysis show the usefulness of the method.

Item Type:	Journal Article
Divisions:	Faculty of Science > Statistics
Journal or Publication Title:	Statistics and Computing
Publisher:	Springer
ISSN:	0960-3174
Official Date:	January 2014
Dates:	Date Event January 2014 Published 17 October 2013 Available 25 September 2012 Accepted 8 March 2012 Submitted
Volume:	Volume 24
Number:	Number 1
Number of Pages:	13
Page Range:	pp. 123-136
DOI:	10.1007/s11222-012-9358-0
Status:	Peer Reviewed
Publication Status:	Published

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