Prediction bounds for (higher order) total variationregularized least squares

04/24/2019

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by   Sara van de Geer, et al.

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We establish oracle inequalities for the least squares estimator f̂ with penalty on the total variation of f̂ or on its higher order differences. Our main tool is an interpolating vector that leads to lower bounds for compatibility constants. This allows one to show that for any N ∈N the N^ th order differences penalty leads to an estimator f̂ that can adapt to the number of jumps in the (N-1)^ th order differences.