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On the Dirichlet-kernel Gasser--Müller estimator and its ...
[Submitted on 12 Feb 2025 (v1), last revised 4 Jul 2026 (this ve · 2025-02-12 · via math.ST updates on arXiv.org

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Abstract:A Dirichlet-kernel Gasser-Müller (D-GM) estimator is introduced for fixed design regression on the simplex, extending the univariate analog due to Chen [Statist. Sinica, vol. 10(1) (2000), pp. 73-91]. Its pointwise bias and variance, asymptotic normality, and mean integrated squared error are investigated. Some simulation experiments are conducted to compare its small-sample performance with that of two recently proposed alternatives: the Dirichlet-kernel Nadaraya-Watson (D-NW) and local linear (D-LL) estimators. The simulation results reveal that the D-LL estimator is best among the D-LL, D-NW, and D-GM estimators and that the proposed D-GM estimator is worst. A real data analysis is also reported for the GEMAS dataset to analyze the relationship between soil composition and pH levels across various agricultural and grazing lands in Europe.

Submission history

From: Frédéric Ouimet [view email]
[v1] Wed, 12 Feb 2025 14:56:01 UTC (247 KB)
[v2] Mon, 20 Apr 2026 19:36:47 UTC (245 KB)
[v3] Sat, 4 Jul 2026 05:36:16 UTC (246 KB)