Mathematics – Statistics Theory
Scientific paper
2011-07-07
Mathematics
Statistics Theory
57 pages, 5 figures, This is a much more general version of previous work with the title: "Multiscale Methods for Shape Constr
Scientific paper
We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We investigate the moderately ill-posed setting, where the Fourier transform of the error density in the deconvolution model is of polynomial decay. For multiscale testing, we consider a calibration, motivated by the modulus of continuity of Brownian motion. We investigate the performance of our results from both the theoretical and simulation based point of view. A major consequence of our work is that the detection of qualitative features of a density in a deconvolution problem is a doable task although the minimax rates for pointwise estimation are very slow.
Duembgen Lutz
Munk Axel
Schmidt-Hieber Johannes
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