Eckle, KonstantinBissantz, NicolaiDette, HolgerProksch, KatharinaEinecke, Sabrina2016-04-122016-04-122016http://hdl.handle.net/2003/3488710.17877/DE290R-16935In 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.enDiscussion Paper / SFB823;14, 2016multiple testsX-ray astronomymultivariate densitymodes310330620working paper