Bayesian surface regression versus spatial spectral nonparametric curve regression

TL;DR

This paper compares Bayesian surface regression and spatial spectral nonparametric curve regression methods for analyzing COVID-19 incidence across Spanish provinces, focusing on their estimation of spatial and temporal correlations.

Contribution

It introduces and compares two infinite-dimensional regression approaches, one Bayesian and one nonparametric, for modeling complex spatiotemporal data.

Findings

Bayesian approach effectively estimates the spectral properties of the temporal autocorrelation.

Spatial spectral regression captures spatial dependence between curves.

Cross-validation shows differences in predictive performance between methods.

Abstract

COVID-19 incidence is analyzed at the provinces of some Spanish Communities during the period February-October, 2020. Two infinite-dimensional regression approaches are tested. The first one is implemented in the regression framework introduced in Ruiz-Medina, Miranda and Espejo (2019). Specifically, a bayesian framework is adopted in the estimation of the pure point spectrum of the temporal autocorrelation operator, characterizing the second-order structure of a surface sequence. The second approach is formulated in the context of spatial curve regression. 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.