Multiscale inference for a multivariate density with applications to X-ray astronomy
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 multivariate 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.
Cite
@article{arxiv.1604.04405,
title = {Multiscale inference for a multivariate density with applications to X-ray astronomy},
author = {Konstantin Eckle and Nicolai Bissantz and Holger Dette and Katharina Proksch and Sabrina Einecke},
journal= {arXiv preprint arXiv:1604.04405},
year = {2016}
}
Comments
Keywords and Phrases: multiple tests, modes, multivariate density, X-ray astronomy AMS Subject Classification: 62G07, 62G10, 62G20