A program that conducts group variable selection for quantile and robust mean regression (Sherwood and Li, 2022). The group lasso penalty (Yuan and Lin, 2006) is used for group-wise variable selection. Both of the quantile and mean regression models are based on the Huber loss. Specifically, with the tuning parameter in the Huber loss approaching to 0, the quantile check function can be approximated by the Huber loss for the median and the tilted version of Huber loss at other quantiles. Such approximation provides computational efficiency and stability, and has also been shown to be statistical consistent.
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