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Executive office, management

Thorsten Ziebach

+49 231 755 - 3122

Melanie Große, geb. Wübbold

+49 231 755 - 5735

spatial and structural adaptation

The fi rst part of the talk is devoted to a brief presentation of one approach to the problem of pointwise adaptive estimation in heteroscedastic regression. The nonparametric model with unknown mean and variance is approximated by a local linear model with incorrectly speci ed covariance matrix. Obviously, such an approximation would be lousy globally, therefore the data-driven choice of the degree of localization plays a crucial role in this approach. Adaptive choice of locality in this set-up can be understood as a selection of an appropriate parametric model from a given collection. As a selection rule a technique based on Lepski's method is developed. The quality of the adaptive estimator is judged in terms of oracle inequalities. The analysis shows that the procedure allows a misspeci cation of the covariance matrix with a relative error of order 1/log(n), where n is the sample size.
The second part of the talk focuses on the ongoing join project with Oleg Lepski (University of Provence Aix-Marseille I) addressed to adaptive estimation in the single-index model with unknown link function and index vector. We show that the problem of adaptive estimation can be interpreted in terms of selection from a family of speci c kernel estimators. A novel procedure for selection from this collection allowing simultaneous adaptation to the unknown structure and the smoothness of the signal is proposed. Using the established for the procedure local oracle inequality we show that the proposed selection rule provides a rate optimal (within the logpayment for pointwise adaptation in the so-called "dense" zone) estimator which is adaptive over the scale of Besov classes.


Spatial and structural adaptation

Speaker: Nora Serdyukova (Université de Provence, LATP - CMI, Marseille, France)

When and where?

Tuesday, Jul 4, 2011  Bochum (4.15 pm, NA 3/64, Fakultät für Mathematik, Ruhr-Universität Bochum)