Multiscale local polynomial density estimation

Maarten Jansen

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 16, 5164-5190

Abstract: The multiscale local polynomial transform (MLPT) is a combination of a kernel method for non parametric regression or density estimation with a projection onto a basis in a multiscale framework. The MLPT is proposed for the estimation of densities with possibly one or more singular points at unknown locations. The proposed estimator reformulates the density estimation problem as a high-dimensional, sparse regression problem with asymptotically exponential response variables. The covariates in this model are the observations from the unknown density themselves. The design matrix comes from a novel extension of the MLPT for use on highly non equidistant data.

Date: 2025
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DOI: 10.1080/03610926.2024.2434933

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