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Optimal adaptive estimation of linear functionals under sparsity
Olivier Collier, Laëtitia Comminges, Alexandre B. Tsybakov +1
We consider the problem of estimation of a linear functional in the Gaussian sequence model where the unknown vector theta in R^d belongs to a class of s-sparse vectors with unknow…
Bounds on the prediction error of penalized least squares estimators with convex penalty
Pierre C. Bellec, Alexandre B. Tsybakov
This paper considers the penalized least squares estimator with arbitrary convex penalty. When the observation noise is Gaussian, we show that the prediction error is a subgaussian…
Slope meets Lasso: improved oracle bounds and optimality
Pierre C. Bellec, Guillaume Lecué, Alexandre B. Tsybakov
We show that two polynomial time methods, a Lasso estimator with adaptively chosen tuning parameter and a Slope estimator, adaptively achieve the exact minimax prediction and $\ell…