Dynamical local Fr\'echet curve regression in manifolds

ArXi:2505.05168v3 Announce Type: replace-cross Under mild conditions, this paper derives a least-squares local linear Fr\'echet curve predictor for response and regressor evaluated in a separable Hilbert space. We obtain the conditions allowing the implementation of this local linear Fr\'echet functional predictor in the ambient L^{2}-space of vector functions, with values in the time-varying tangent space on a compact Riemannian manifold. An intrinsic local linear Fr\'echet curve predictor evaluated in such a manifold is secondly proposed, based on a weighted Fr\'echet mean approach.