Economics at your fingertips  

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

Konstantin Eckle, Nicolai Bissantz, Holger Dette (), Katharina Proksch and Sabrina Einecke
Additional contact information
Konstantin Eckle: Ruhr-Universität Bochum
Nicolai Bissantz: Ruhr-Universität Bochum
Holger Dette: Ruhr-Universität Bochum
Katharina Proksch: Georg-August-Universität Göttingen
Sabrina Einecke: Technische Universität Dortmund

Annals of the Institute of Statistical Mathematics, 2018, vol. 70, issue 3, 647-689

Abstract: 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 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.

Keywords: Multiple tests; Modes; Multivariate density; X-ray astronomy (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed

Downloads: (external link) Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link:

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10463/PS2

Access Statistics for this article

Annals of the Institute of Statistical Mathematics is currently edited by Tomoyuki Higuchi

More articles in Annals of the Institute of Statistical Mathematics from Springer, The Institute of Statistical Mathematics
Bibliographic data for series maintained by Sonal Shukla ().

Page updated 2019-11-06
Handle: RePEc:spr:aistmt:v:70:y:2018:i:3:d:10.1007_s10463-017-0605-1