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arXiv · 2408.07209

Local linear smoothing for regression surfaces on the simplex using Dirichlet kernels

Christian Genest·Frédéric Ouimet
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Abstract

This paper introduces a local linear smoother for regression surfaces on the simplex. The estimator solves a least-squares regression problem weighted by a locally adaptive Dirichlet kernel, ensuring good boundary properties. Asymptotic results for the bias, variance, mean squared error, and mean integrated squared error are derived, generalizing the univariate results of Chen [Ann. Inst. Statist. Math., 54(2) (2002), pp. 312-323]. A simulation study shows that the proposed local linear estimator with Dirichlet kernel outperforms its only direct competitor in the literature, the Nadaraya-Watson estimator with Dirichlet kernel due to Bouzebda, Nezzal and Elhattab [AIMS Math., 9(9) (2024), pp. 26195-26282].

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Christian Genest, Frédéric Ouimet. 2025-05-11. Local linear smoothing for regression surfaces on the simplex using Dirichlet kernels. https://doi.org/10.1007/s00362-025-01708-8

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