Wavelet regression for compositional data

• A. Srakar ^[1] ; T.R.L. Fry ^[2]
  1. [1] Institute for Economic Research and University of Ljubljana, Ljubljana, Slovenia
  2. [2] RMIT University, Melbourne, Australia
• Localización: Proceedings of the 8th International Workshop on Compositional Data Analysis (CoDaWork2019): Terrassa, 3-8 June, 2019 / Juan José Egozcue Rubí (aut.), Jan Graffelman (aut.), María Isabel Ortego Martínez (aut.), 2019, ISBN 978-84-947240-2-2, págs. 151-156
• Idioma: inglés
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• Resumen

  • Regression for compositional data has so far been largely considered only from a parametric point of view. Recently, some work adapted non-parametric regression to nonEuclidean manifolds. For example, Di Marzio et al. (2013) pursue the circular case, and Di Marzio et al. (2014) the spherical one. In a recent article, Di Marzio, Panzera and Venieri (2015) extended this to nonparametric situations, introducing local constant and local linear smoothing for regression with compositional data. Also, Barientos et al. (2015) propose a Bayesian nonparametric procedure for density estimation for data in a d-dimensional simplex. In our analysis, we extend the work of Di Marzio, Panzera and Venieri to locally adaptive estimators, in particular discrete and continuous wavelets. We rely on the work of Dey and Wang (2004), modeling the priors on triangles by use of wavelets constructed specifically for triangles. We transfer their methodology of deriving father and motherwavelets using a sequential approach to orthogonalization to derive the motherwavelets. Our new estimator is derived for three cases: simplicial-real; simplicial-simplicial; and real-simplicial regression and is based on Bayesian approach using wavelet type priors. We present a detailed statistical elaboration and analysis, simulation results to compare the performance with some existing parametric estimators for compositional data regression, and an application to the results to two case studies from economics– inference for inequality indices and international trade.