A0730
Title: Wavelet regression for symplectic data from a Bayesian and nonparametric Bayes perspective
Authors: Andrej Srakar - Institute for Economic Research Ljubljana (Slovenia) [presenting]
Abstract: Regression for symplectic, i.e. compositional data, has so far been largely considered only from a parametric point of view. It has also been extended to nonparametric situations, introducing local constant and local linear smoothing for regression with compositional data and simplicial splines. We extend their analysis to wavelet regressions, constructing wavelet transforms, deriving father and mother wavelets using Legendre polynomial based sequential approach to orthogonalization. We extend their perspective for wavelet construction in any topological and symplectic space, enabling its usage for modelling compositional data of any dimension. To derive the wavelet regression estimator, we use a Bayesian approach, namely multivariate wavelet priors, evaluating the fit with a recent Stein-based procedure. We extend this further to the nonparametric Bayes perspective using random Bernstein polynomials. The new regression estimators are derived for all three cases: simplicial-real, simplicial-simplicial, and real-simplicial regression. The performance of the estimators is studied in delta-type asymptotic analysis and simulation study. We apply the findings to two economic datasets on income inequality and international trade.
