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Regularized simultaneous model selection in multiple quantiles regression

  • Zou, Hui
  • Yuan, Ming
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    Simultaneously estimating multiple conditional quantiles is often regarded as a more appropriate regression tool than the usual conditional mean regression for exploring the stochastic relationship between the response and covariates. When multiple quantile regressions are considered, it is of great importance to share strength among them. In this paper, we propose a novel regularization method that explores the similarity among multiple quantile regressions by selecting a common subset of covariates to model multiple conditional quantiles simultaneously. The penalty we employ is a matrix norm that encourages sparsity in a column-wise fashion. We demonstrate the effectiveness of the proposed method using both simulations and an application of gene expression data analysis.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(08)00273-9
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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 52 (2008)
    Issue (Month): 12 (August)
    Pages: 5296-5304

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    Handle: RePEc:eee:csdana:v:52:y:2008:i:12:p:5296-5304
    Contact details of provider: Web page: http://www.elsevier.com/locate/csda

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    1. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67.
    2. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    3. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    4. Koenker R. & Geling O., 2001. "Reappraising Medfly Longevity: A Quantile Regression Survival Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 458-468, June.
    5. Li, Youjuan & Liu, Yufeng & Zhu, Ji, 2007. "Quantile Regression in Reproducing Kernel Hilbert Spaces," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 255-268, March.
    6. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521608275, june. pag.
    7. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
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