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    $\begingroup$ Quantile regression has a loss function. $$ L_{\tau}(y_i, \hat y_i) = \begin{cases} \tau\vert y_i - \hat y_i\vert, & y_i - \hat y_i \ge 0 \\ (1 - \tau)\vert y_i - \hat y_i\vert, & y_i - \hat y_i < 0 \end{cases} $$ (Then you add up the values for each index $i$ to get a loss for the entire regression, same as you would for absolute loss or square loss.) Why not use it? $\endgroup$ Commented Jun 27, 2022 at 15:48