Minimax properties of Dirichlet kernel density estimators
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This paper is concerned with the asymptotic behavior in β-Hölder 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 ∈ [1, 3) and β∈ (0, 2], and that it is never minimax when p ∈ [4, ∞) or β∈ (2, ∞). 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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