Non-parametric regression for compositional data. (April 2015)

• Record Type: Journal Article
• Authors: Di Marzio, Marco; Panzera, Agnese; Venieri, Catia
• Other Names: Filzmoser Peter guest-editor.; Hron Karel guest-editor.
• Is Part Of: Statistical modelling. Volume 15:Number 2(2015)
• Page Start: 113
• Page End: 133
• Publication Date: 2015-04
• Subjects: isometric log-ratio (ilr) transformation -- local constant fit -- local linear fit -- simplicial kernels -- soil composition; Linear models (Statistics) -- Periodicals; Mathematical models -- Periodicals; Modèles linéaires (Statistique) -- Périodiques; Modèles mathématiques -- Périodiques; Modèle statistique; Modèle linéaire; Modélisation statistique; Périodique électronique (Descripteur de forme); Ressource Internet (Descripteur de forme); 519.5011
• DOI: 10.1177/1471082X14535522
• Languages: English
• ISSNs: 1471-082X

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.