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An efficient algorithm for structured sparse quantile regression

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  • Vahid Nassiri
  • Ignace Loris

Abstract

An efficient algorithm is derived for solving the quantile regression problem combined with a group sparsity promoting penalty. The group sparsity of the regression parameters is achieved by using a $$\ell _{1,\infty }$$ ℓ 1 , ∞ -norm penalty (or constraint) on the regression parameters. The algorithm is efficient in the sense that it obtains the regression parameters for a wide range of penalty parameters, thus enabling easy application of a model selection criteria afterwards. A Matlab implementation of the proposed algorithm is provided and some applications of the methods are studied. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Vahid Nassiri & Ignace Loris, 2014. "An efficient algorithm for structured sparse quantile regression," Computational Statistics, Springer, vol. 29(5), pages 1321-1343, October.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:5:p:1321-1343
    DOI: 10.1007/s00180-014-0494-1
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    References listed on IDEAS

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    1. Cathy Chen & Richard Gerlach, 2013. "Semi-parametric quantile estimation for double threshold autoregressive models with heteroskedasticity," Computational Statistics, Springer, vol. 28(3), pages 1103-1131, June.
    2. Rahim Alhamzawi & Keming Yu, 2012. "Variable selection in quantile regression via Gibbs sampling," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(4), pages 799-813, August.
    3. Chen, Cathy W.S. & Gerlach, Richard & Wei, D.C.M., 2009. "Bayesian causal effects in quantiles: Accounting for heteroscedasticity," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 1993-2007, April.
    4. R. Alhamzawi & K. Yu & D. F. Benoit, 2011. "Bayesian adaptive Lasso quantile regression," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 11/728, Ghent University, Faculty of Economics and Business Administration.
    5. Jason Boardman & Daniel Powers & Yolanda Padilla & Robert Hummer, 2002. "Low birth weight, social factors, and developmental outcomes among children in the United States," Demography, Springer;Population Association of America (PAA), vol. 39(2), pages 353-368, May.
    6. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, September.
    7. Douglas Almond & Kenneth Y. Chay & David S. Lee, 2005. "The Costs of Low Birth Weight," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 120(3), pages 1031-1083.
    8. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    9. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    10. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258, January.
    11. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
    12. 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, February.
    13. Zou, Hui & Yuan, Ming, 2008. "Regularized simultaneous model selection in multiple quantiles regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5296-5304, August.
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