Electronic Journal of Statistics

Multiscale inference for multivariate deconvolution

Konstantin Eckle, Nicolai Bissantz, and Holger Dette

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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.

Article information

Electron. J. Statist., Volume 11, Number 2 (2017), 4179-4219.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G07: Density estimation 62G10: Hypothesis testing
Secondary: 62G20: Asymptotic properties

Deconvolution modes multivariate density multiple tests Gaussian approximation

Creative Commons Attribution 4.0 International License.


Eckle, Konstantin; Bissantz, Nicolai; Dette, Holger. Multiscale inference for multivariate deconvolution. Electron. J. Statist. 11 (2017), no. 2, 4179--4219. doi:10.1214/17-EJS1355. https://projecteuclid.org/euclid.ejs/1508983572

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