Multiscale inference for a multivariate density with applications to X-ray astronomy
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Date
2016
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Abstract
In this paper we propose methods for inference of the geometric features of a multivariate density. Our approach uses multiscale tests for the monotonicity of the density
at arbitrary points in arbitrary directions. In particular, a significance test for a mode at
a specific point is constructed. Moreover, we develop multiscale methods for identifying
regions of monotonicity and a general procedure for detecting the modes of a multivari-
ate density. It is is shown that the latter method localizes the modes with an effectively
optimal rate. The theoretical results are illustrated by means of a simulation study and
a data example. The new method is applied to and motivated by the determination
and verification of the position of high-energy sources from X-ray observations by the
Swift satellite which is important for a multiwavelength analysis of objects such as Active
Galactic Nuclei.
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Keywords
multiple tests, X-ray astronomy, multivariate density, modes