Journal
JOURNAL OF MULTIVARIATE ANALYSIS
Volume 91, Issue 1, Pages 74-89Publisher
ELSEVIER INC
DOI: 10.1016/j.jmva.2004.05.006
Keywords
quantile regression; penalty methods; shrinkage; L-statistics; random effects; robust estimation; hierarchical models
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The penalized least squares interpretation of the classical random effects estimator suggests a possible way forward for quantile regression models with a large number of fixed effects. The introduction of a large number of individual fixed effects can significantly inflate the variability of estimates of other covariate effects. Regularization, or shrinkage of these individual effects toward a common value can help to modify this inflation effect. A general approach to estimating quantile regression models for longitudinal data is proposed employing l(1) regularization methods. Sparse linear algebra and interior point methods for solving large linear programs are essential computational tools. (C) 2004 Elsevier Inc. All rights reserved.
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