Corrected proof of the result of 'a prediction error property of the Lasso estimator and its generalization' by Huang (2003)

The Lasso achieves variance reduction and variable selection by solving an ℓ1-regularized least squares problem. Huang (2003) claims that 'there always exists an interval of regularization parameter values such that the corresponding mean squared prediction error for the Lasso estimator is smaller than for the ordinary least square estimator'. This result is correct. However, its proof in Huang (2003) is not. This paper presents a corrected proof of the claim, which exposes and uses some interesting fundamental properties of the Lasso.