On the Dirichlet-kernel Gasser--M\"uller estimator and its competitors for fixed design regression on the simplex
Abstract
A Dirichlet-kernel Gasser-M\"uller (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.
Cite
@article{arxiv.2502.08461,
title = {On the Dirichlet-kernel Gasser--M\"uller estimator and its competitors for fixed design regression on the simplex},
author = {Hanen Daayeb and Christian Genest and Salah Khardani and Nicolas Klutchnikoff and Frédéric Ouimet},
journal= {arXiv preprint arXiv:2502.08461},
year = {2026}
}
Comments
18 pages, 2 figures, 1 table