@misc{10481/104253,
year = {2025},
month = {4},
url = {https://hdl.handle.net/10481/104253},
abstract = {Global Fréchet regression is addressed from the observation of a strictly stationary
bivariate curve process, evaluated in a finite-dimensional compact differentiable Riemannian
manifold with bounded positive smooth sectional curvature. The involved
univariate curve processes respectively define the functional response and regressor,
having the same Fréchet functional mean. The supports of the marginal probability
measures of the regressor and response processes are assumed to be contained in a
ball, whose radius ensures the injectivity of the exponential map. This map has a timevarying
origin at the common marginal Fréchet functional mean. A weighted Fréchet
mean approach is adopted in the definition of the theoretical loss function. The regularized
Fréchet weights are computed in the time-varying tangent space from the
log-mapped regressors. Under these assumptions, and some Lipschitz regularity sample
path conditions, when a unique minimizer exists, the uniform weak-consistency
of the empirical Fréchet curve predictor is obtained, under mean-square ergodicity
of the log-mapped regressor process in the first two moments. A simulated example
in the sphere illustrates the finite sample size performance of the proposed Fréchet
predictor. Predictions in time of the spherical coordinates of the magnetic field vector
are obtained from the time-varying geocentric latitude and longitude of the satellite
NASA’s MAGSAT spacecraft in the real-data example analyzed.},
organization = {Funding for open access charge: Universidad de Granada / CBUA},
organization = {MCIN/ AEI/PID2022-142900NB-I00, MCIN/ AEI/PGC2018-099549-B-I00},
organization = {CEX2020-001105-M MCIN/AEI/ 10.13039/501100011033},
publisher = {Springer Nature},
keywords = {Fréchet functional regression},
keywords = {Riemannian manifold},
keywords = {Time correlated manifold-valued bivariate curve data},
title = {Global Fréchet regression from time correlated bivariate curve data inmanifolds},
doi = {10.1007/s00362-025-01684-z},
author = {Torres Signes, Antoni and Frías, M. P. and Ruiz Medina, María Dolores},
}