Multiscale inference for multivariate deconvolution
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Date
2016
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Abstract
In this paper we provide new methodology for inference of the geometric features of
a multivariate density in deconvolution. Our approach is based on multiscale tests to
detect significant directional derivatives of the unknown density at arbitrary points in
arbitrary directions. The multiscale method is used to identify regions of monotonicity
and to construct a general procedure for the detection of modes of the multivariate density.
Moreover, as an important application a significance test for the presence of a local
maximum at a pre-specified point is proposed. The performance of the new methods is investigated
from a theoretical point of view and the finite sample properties are illustrated
by means of a small simulation study.
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Keywords
deconvolution, Gaussian approximation, multiple tests, multivariate density, modes