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Adaptive estimation with soft thresholding penalties. (English) Zbl 1090.62534

Summary: 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.

MSC:

62G08 Nonparametric regression and quantile regression
62G35 Nonparametric robustness
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