On the Dirichlet-kernel Gasser--M\"uller estimator and its competitors for fixed design regression on the simplex

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.