2 problems

Let $\ell_{\alpha}(u)=\alpha u$ for $u\geq 0$ and $(\alpha-1)u$ for $u<0$ be the pinball loss, let $\hat{\eta}_{n+1}$ be the dual quantile-regression score, and let…

Let $(X_i,Y_i)_{i=1}^{n+1}$ follow the data-generating process described in Section 2, let $\hat{\beta}$ be the LASSO estimator fit on all $n+1$ observations, and let…