Nonparametric regression for compositional data

We introduce local constant and local linear regression smoothing for 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.