Multiscale inference for a multivariate density with applications to X-ray astronomy (Q1753976)

A multiscale method is presented to identify regions of monotonicity of a multivariate density at arbitrary points in arbitrary directions. The approach of \textit{L. Dümbgen} and \textit{G. Walther} [Ann. Stat. 36, No. 4, 1758--1785 (2008; Zbl 1142.62336)] is extended to the situation where no prior information regarding the location and the number of the modes is available. In particular, a significance test for a mode at a specific point is constructed and a general procedure is developed for detecting the modes of a multivariate density. It is shown that the method localizes the modes with an effectively optimal rate. The results are illustrated in simulation study and a data example from X-ray astronomy.