Interquantile shrinkage and variable selection in quantile regression

Examination of multiple conditional quantile functions provides a comprehensive view of the relationship between the response and covariates. In situations where quantile slope coefficients share some common features, estimation efficiency and model interpretability can be improved by utilizing such...

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Bibliographic Details
Published in:Computational statistics & data analysis 2014-01, Vol.69, p.208-219
Main Authors: Jiang, Liewen, Bondell, Howard D., Wang, Huixia Judy
Format: Article
Language:English
Subjects:
Commonality
Data processing
Fused adaptive Lasso
Fused adaptive sup-norm
Mathematical analysis
Mathematical models
motivation
Oracle
Quantile regression
Quantiles
Regression
regression analysis
Shrinkage
Smoothing
Statistics
Variable selection
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Summary:Examination of multiple conditional quantile functions provides a comprehensive view of the relationship between the response and covariates. In situations where quantile slope coefficients share some common features, estimation efficiency and model interpretability can be improved by utilizing such commonality across quantiles. Furthermore, elimination of irrelevant predictors will also aid in estimation and interpretation. These motivations lead to the development of two penalization methods, which can identify the interquantile commonality and nonzero quantile coefficients simultaneously. The developed methods are based on a fused penalty that encourages sparsity of both quantile coefficients and interquantile slope differences. The oracle properties of the proposed penalization methods are established. Through numerical investigations, it is demonstrated that the proposed methods lead to simpler model structure and higher estimation efficiency than the traditional quantile regression estimation.
ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2013.08.006