Kernel density estimation by stagewise algorithm with a simple dictionary

Kiheiji Nishida () and Kanta Naito ()
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Kiheiji Nishida: Hyogo Medical University
Kanta Naito: Chiba University

Computational Statistics, 2024, vol. 39, issue 2, No 6, 523-560

Abstract: Abstract This study proposes multivariate kernel density estimation by stagewise minimization algorithm based on U-divergence and a simple dictionary. The dictionary consists of an appropriate scalar bandwidth matrix and a part of the original data. The resulting estimator brings us data-adaptive weighting parameters and bandwidth matrices, and provides a sparse representation of kernel density estimation. We develop the non-asymptotic error bound of the estimator that we obtained via the proposed stagewise minimization algorithm. It is confirmed from simulation studies that the proposed estimator performs as well as, or sometimes better than, other well-known density estimators.

Keywords: Kernel density estimation; Stagewise minimization algorithm; Dictionary; U-divergence; Data condensation (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00180-022-01303-7

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