Multiscale inference for multivariate deconvolution

TL;DR

This paper introduces a multiscale inference methodology for analyzing the geometric features of multivariate densities in deconvolution, enabling detection of features like modes and local maxima.

Contribution

It develops new multiscale testing procedures for identifying geometric features of multivariate densities in deconvolution, including modes and local maxima detection.

Findings

The methods are supported by theoretical analysis.

Finite sample properties are demonstrated through simulations.

Abstract

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.