Multiscale Methods for Shape Constraints in Deconvolution

摘要: We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is test local monotonicity on all scales simultaneously. investigate moderately ill-posed setting, where Fourier transform error density model polynomial decay. For testing, we consider a calibration, motivated by modulus continuity Brownian motion. performance our results from both theoretical and simulation based point view. A major consequence work that detection problem doable task although minimax rates pointwise estimation are very slow.