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2017 Multiscale inference for multivariate deconvolution
Konstantin Eckle, Nicolai Bissantz, Holger Dette
Electron. J. Statist. 11(2): 4179-4219 (2017). DOI: 10.1214/17-EJS1355


In this paper we provide new methodology for inference of the geometric features of a multivariate density in deconvolution. Our approach is based on multiscale tests to detect significant directional derivatives of the unknown density at arbitrary points in arbitrary directions. The multiscale method is used to identify regions of monotonicity and to construct a general procedure for the detection of modes of the multivariate density. Moreover, as an important application a significance test for the presence of a local maximum at a pre-specified point is proposed. The performance of the new methods is investigated from a theoretical point of view and the finite sample properties are illustrated by means of a small simulation study.


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Konstantin Eckle. Nicolai Bissantz. Holger Dette. "Multiscale inference for multivariate deconvolution." Electron. J. Statist. 11 (2) 4179 - 4219, 2017.


Received: 1 November 2016; Published: 2017
First available in Project Euclid: 26 October 2017

zbMATH: 1380.62143
MathSciNet: MR3716498
Digital Object Identifier: 10.1214/17-EJS1355

Primary: 62G07 , 62G10
Secondary: 62G20

Keywords: Deconvolution , Gaussian approximation , modes , multiple tests , multivariate density


Vol.11 • No. 2 • 2017
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