A. Torres Signes, M. D. RUIZ-MEDINA
In the present work, we consider Fréchet intrinsic and extrinsic geodesic curve regression from Riemmanian manifold-valued bivariate curve data correlated in time. Both regression frameworks are of interest in several fields of application like world magnetic models generated from remote sensors. These manifold curve prediction methodologies are illustrated in a comparative study by simulations. A real bivariate curve data set, available in NASA's National Space Science Data Center, is analyzed to evaluate the performance of both functional regression methodologies. Specifically, the time-varying spherical coordinates of the Earth's magnetic field are predicted, from the geocentric latitude and longitude of the satellite NASA's MAGSAT spacecraft. The methodology of 5-fold random cross-validation is implemented in this real data analysis.
Keywords: Extrinsic regression, Intrinsic regression, Manifold-valued curve processes, Riemannian manifold.
Scheduled
Spatio-Temporal Statistics I
June 11, 2025 3:30 PM
MR 3