Non-parametric regression for compositional data

Abstract

Regression for compositional data has been considered only from a parametric point of view. We introduce local constant and local linear smoothing for this problem, and treat the cases when the response, the predictor or both of them are compositions. To this end, we introduce suitable series expansions of the regression function at a point, along with a class of simplicial kernels. Our methods are formulated according to the Aitchison geometry of the simplex and then, using some relevant properties of the isometric log-ratio transformation, are developed following the principle of ‘working on coordinates’. Asymptotic properties and real-data case studies show the effectiveness of the methods.