A0713
Title: Extrinsic and intrinsic local linear regression from time correlated bivariate curve data
Authors: Maria Dolores Ruiz-Medina - University of Granada (Spain) [presenting]
Abstract: The purpose is to extend local linear regression to the context of bivariate curve data correlated in time. This problem is addressed by adopting a weighted Frechet mean approach when the response and the regressors are evaluated in a separable Hilbert space. Hereafter, the results derived are applied to extrinsic local linear Frechet regression from time-correlated bivariate curve data evaluated in a compact Riemannian manifold via the time-varying tangent space under suitable geometrical, regularity, and probabilistic conditions. Alternatively, an intrinsic local linear curve Frechet regression approach is adopted in the manifold under the same setting of conditions. This Frechet predictor involves nonlinear geodesic weights. The optimality of this predictor, approximating the conditional curve Frechet mean, is also analyzed. In the simulation study undertaken, a performance comparative study of the two proposed local linear curve predictors is achieved from finite curve samples in the manifold. A bandwidth parameter analysis is carried out under different model scenarios. An application to functional prediction of the spherical coordinates of the magnetic field vector from the time-varying geocentric latitude and longitude of the satellite NASA MAGSAT spacecraft is also addressed.
