Local regression for compositional data

Regression for compositional data has been considered only from a parametric point of view. We introduce a nonparametric estimator for the regression function when both the response variable and the predictor can be defined on the simplex, and derive its asymptotic properties. To this end, we use the isometric log-ratio transformation along with properly defined kernel functions. The performances of our estimator are compared to those of a parametric model using a real data set.