Bayesian surface regression versus spatial spectral nonparametric curve regression Ruiz Medina, María Dolores Miranda, Doris Bayesian estimation Nonparametric estimation Spatial curve regression Spatial periodogram operator Spatial spectral density operator Surface regression COVID{19 incidence is analyzed at the provinces of some Spanish Communities during the period February{October, 2020. Two in nite{ dimensional regression approaches are tested. The rst one is implemented in the regression framework introduced in Ruiz{Medina, Miranda and Espejo [70]. Speci cally, 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. 2022-09-08T07:23:49Z 2022-09-08T07:23:49Z 2021-10-30 journal article Published version: M.D. Ruiz–Medina, D. Miranda, Bayesian surface regression versus spatial spectral nonparametric curve regression, Spatial Statistics, Volume 50, 2022, 100604, ISSN 2211-6753, [https://doi.org/10.1016/j.spasta.2022.100604] http://hdl.handle.net/10481/76572 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional Elsevier