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 \(\ell _{1,\infty }\)-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.
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Acknowledgments
I.L. is a research associate of the F.R.S.-FNRS (Belgium). This research was supported by VUB GOA-062 and by the FWO-Vlaanderen grant G.0564.09N.
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Nassiri, V., Loris, I. An efficient algorithm for structured sparse quantile regression. Comput Stat 29, 1321–1343 (2014). https://doi.org/10.1007/s00180-014-0494-1
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DOI: https://doi.org/10.1007/s00180-014-0494-1