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

Christian Genest () and Frédéric Ouimet ()
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Christian Genest: McGill University
Frédéric Ouimet: McGill University

Statistical Papers, 2025, vol. 66, issue 4, No 24, 28 pages

Abstract: 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 Stat Math, 54(2):312–323, 2002). 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 et al. (AIMS Math 9(9):26195–26282, 2024).

Keywords: Adaptive estimator; Asymmetric kernel; Beta kernel; Boundary bias; Dirichlet kernel; Local linear smoother; Mean integrated squared error; Nadaraya–Watson estimator; Nonparametric regression; Regression surface; Simplex; Primary: 62G08; Secondary: 62G05; 62H12 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00362-025-01708-8

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