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Adaptive asymptotically efficient estimation in heteroscedastic nonparametric regression. (English) Zbl 1293.62091

Summary: The paper considers some asymptotic properties of the adaptive procedure proposed in the authors’ paper [“Adaptive nonparametric estimation in heteroscedastic regression models. I: Sharp non-asymptotic oracle inequalities”, J. Nonparametric Stat. 21, No. 1, 1–16 (2009), http://hal.archives-ouvertes.fr/hal-00269196] for estimating an unknown nonparametric regression. We show that the procedure is asymptotically efficient for quadratic risk, i.e. the asymptotic quadratic risk of the procedure coincides with the corresponding Pinsker constant provided the sharp lower bound for the quadratic risk over all possible estimators.

MSC:

62G08 Nonparametric regression and quantile regression
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
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