The <Square-root Lasso> estimator with regularization parameter $\gamma>0$ is
$$
\widehat\beta
=\underset{\beta\in\mathbb R^p}{\operatorname{argmin}}
\left\{\frac1{\sqrt n}\lVert Y-X\beta\rVert_2+\gamma\lVert\beta\rVert_1\right\}.
$$
Unlike the ordinary <Lasso>, its tuning parameter does not require prior knowledge of the noise standard deviation $\sigma$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 205 / 4 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-205/4/a/solution