A. Torres-Signes

M. D. Ruiz-Medina, A. Torres-Signes

The present paper solves the problem of local linear approximation of the Fréchet conditional mean in an extrinsic and intrinsic way from time correlated bivariate curve data evaluated in a manifold (see Torres et al, 2025, on global Fréchet functional regression in manifolds). The extrinsic local linear Fréchet functional regression predictor is obtained in the time-varying tangent space by projection into an orthornormal eigenfunction basis in the ambient Hilbert space. The conditions assumed ensure the existence and uniqueness of this predictor, and its computation via exponential and logarithmic maps. A weighted Fréchet mean approach is adopted in the computation of an intrinsic local linear Fréchet functional regression predictor. The asymptotic optimality of this intrinsic local approximation is also proved. The finite sample size performance of the empirical version of both, extrinsic and intrinsic local functional predictors, and of a Nadaraya-Watson type Fréchet curve predictor is illustrated in the simulation study undertaken. As motivating real data application, we consider the prediction problem of the Earth's magnetic field from the time-varying geocentric latitude and longitude of the satellite NASA's MAGSAT spacecraft.

A. Torres-Signes, M. P. Frías, M. D. Ruiz-Medina

A multiple objective space-time forecasting approach is presented involving cyclical curve log-regression, and multivariate time series spatial residual correlation analysis. Specifically, the mean quadratic loss function is minimized in the framework of trigonometric regression. While, in our subsequent spatial residual correlation analysis, maximization of the likelihood allows us to compute the posterior mode in a Bayesian multivariate time series soft-data framework. The presented approach is applied to the analysis of COVID-19 mortality in the first wave affecting the Spanish Communities, since March, 8, 2020 until May, 13, 2020. An empirical comparative study with Machine Learning (ML) regression, based on random k-fold cross-validation, and bootstrapping confidence interval and probability density estimation, is carried out. This empirical analysis also investigates the performance of ML regression models in a hard- and soft- data frameworks. The results could be extrapolated to other counts, countries, and posterior COVID-19 waves.