quantile regression with LASSO penalty

[tclark]

Has anyone written code to estimate quantile regression with LASSO penalty? Evidently there are R code packages for the estimation, but I haven't found anything in the RATS Forum. (RATS does of course have quantile capability through RREG, and Tom has previously made available a LASSO example with linear regression). It seems as though the typical computational reference is Youjuan Li and Ji Zhu (2008), "L1-Norm Quantile Regression," Journal of Computational and Graphical Statistics, Vol. 17, No. 1, pp. 163-185. A widely cited paper with supporting theory in a high dimensional setting is Belloni, Alexandre; Chernozhukov, Victor. ℓ 1 -penalized quantile regression in high-dimensional sparse models. Ann. Statist. 39 (2011), no. 1, 82--130. doi:10.1214/10-AOS827. https://projecteuclid.org/euclid.aos/1291388370.

Thanks much

[tclark]

In the perhaps unlikely event anyone else has an interest in this, I have now put together a QR-LASSO implementation, building off of the LASSO example provided with RATS. Tom -- any suggestions you have to make this more efficient or speed it up (this linear solution is pretty slow with the monthly data example) would be great, should this be obvious to you. There seem to be many write-ups of QR solutions and their variants, but not so transparent (to me, anyway) in implementation.