Adaptive estimation with soft thresholding penalties

Jean–Michel Loubes and Sara Van De Geer

Statistica Neerlandica, 2002, vol. 56, issue 4, 453-478

Abstract: We show that various robust nonparametric regression estimators, such as the least absolute deviations estimator, can be made adaptive (up to logarithmic factors), by adding a soft thresholding type penalty to the loss function. As an example, we consider the situation where the roughness of the regression function is described by a single parameter p. The theory is complemented with a simulation study.

Date: 2002
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