Additive regression with some metric-space-valued predictors and Hilbertian responses

Résumé

Nonparametric additive regression model with some metric-space-valued predictors and Hilbert-space-valued responses is considered. The predictors we consider include finite-dimensional-Hilbert-space-valued predictors and Riemannian-manifold-valued predictors. Those predictors include not only standard Euclidean predictors but also compositional, circular, spherical and shape predictors. The responses we consider include functional responses, density-valued responses, compositional responses and Euclidean responses. For the estimation of the additive model, we apply the smooth backfitting method. We present a complete asymptotic theory including rates of convergence and asymptotic distribution. Our numerical study shows its superior performance and wide applications.