Multiscale inference for multivariate deconvolution
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Date
2016
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Abstract
We propose multiscale tests for deconvolution in order to detect geometric features of
an unknown multivariate density. Our approach uses simultaneous tests on all scales for
the monotonicity of the density at arbitrary points in arbitrary directions. We consider
the situation of polynomial decay of the Fourier transform of the error density in the de-
convolution model (moderately ill-posed). We develop multiscale methods for identifying
regions of monotonicity and a general procedure to detect the modes of a multivariate
density. The theoretical results are illustrated by means of a simulation study.
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Keywords
multiple tests, X-ray astronomy, multivariate density, modes