B0344
Title: Bump detection in heterogeneous Gaussian regression
Authors: Farida Enikeeva - University of Poitiers, Laboratoire de Mathematiques et Applications (France) [presenting]
Axel Munk - University of Goettingen (Germany)
Frank Werner - Max Planck Institute for Biophysical Chemistry (Germany)
Abstract: We consider the problem of the bump detection problem of a signal in a heterogeneous Gaussian regression model. We allow for a simultaneous change in mean and in variance of the signal and specify its impact on the difficulty to detect the null signal against a single bump. We derive lower and upper bounds of testing that lead to explicit characterizations of the detection boundary in several subregimes depending on the asymptotic behavior of the bump heights in mean and variance. In particular, we explicitly identify those regimes, where the additional information about a simultaneous bump in variance eases the detection problem. This effect is made explicit in the constant and the rate, appearing in the detection boundary. We also discuss the case of an unknown bump height and provide an adaptive test in that case.
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