Minimax properties of Dirichlet kernel density estimators - l'unam - université nantes angers le mans
Journal Articles Journal of Multivariate Analysis Year : 2023

Minimax properties of Dirichlet kernel density estimators

Abstract

This paper is concerned with the asymptotic behavior in $\beta$-H\"older spaces and under $L^p$ losses of a Dirichlet kernel density estimator introduced by Aitchison & Lauder (1985) and studied theoretically by Ouimet & Tolosana-Delgado (2021). It is shown that the estimator is minimax when $p \in [1, 3)$ and $\beta \in (0, 2]$, and that it is never minimax when $p \in [4, \infty)$ or $\beta \in (2, \infty)$. These results rectify in a minor way and, more importantly, extend to all dimensions those already reported in the univariate case by Bertin & Klutchnikoff (2011).
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hal-03468285 , version 1 (16-09-2024)

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Karine Bertin, Christian Genest, Frédéric Ouimet, Nicolas Klutchnikoff. Minimax properties of Dirichlet kernel density estimators. Journal of Multivariate Analysis, 2023, 195, pp.105158. ⟨10.1016/j.jmva.2023.105158⟩. ⟨hal-03468285⟩
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