Local linear smoothing for regression surfaces on the simplex using Dirichlet kernels
Statistics Theory
2025-07-22 v4 Applications
Methodology
Statistics Theory
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].
Cite
@article{arxiv.2408.07209,
title = {Local linear smoothing for regression surfaces on the simplex using Dirichlet kernels},
author = {Christian Genest and Frédéric Ouimet},
journal= {arXiv preprint arXiv:2408.07209},
year = {2025}
}
Comments
25 pages, 4 tables, 3 figures