Bayesian surface regression versus spatial spectral nonparametric curve regression

COVID-19 incidence is analyzed at the provinces of the Spanish Communities in the Iberian Peninsula during the period February-October, 2020. Two infinite-dimensional regression approaches, surface regression and spatial curve regression, are proposed. In the first one, Bayesian maximum a posteriori (MAP) estimation is adopted in the approximation of the pure point spectrum of the temporal regression residual autocorrelation operator. Thus, an alternative to the moment-based estimation methodology developed in Ruiz-Medina, Miranda and Espejo (2019) is derived. Additionally, spatial curve regression is considered. A nonparametric estimator of the spectral density operator, based on the spatial periodogram operator, is computed to approximate the spatial correlation between curves. Dimension reduction is achieved by projection onto the empirical eigenvectors of the long-run spatial covariance operator. Cross-validation procedures are implemented to test the performance of the two functional regression approaches.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This study analyzes the incidence of COVID-19 in the provinces of the Spanish Communities in the Iberian Peninsula from February to October 2020. Two infinite-dimensional regression approaches, surface regression and spatial curve regression, are proposed.