Exercise
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Assume that the linear model holds where [math]\eps\sim \sg_n(\sigma^2)[/math]. Moreover, assume the conditions of Theorem and that the columns of [math]X[/math] are normalized in such a way that [math]\max_j|\X_j|_2\le \sqrt{n}[/math]. Then the Lasso estimator [math]\thetalasso[/math] with regularization parameter
satisfies
with probability [math]1-(2d)^{-1}[/math] for some constant [math]C[/math] to be specified.