# Local Fr'echet functional regression in manifolds from time-correlated bivariate curve data

arXiv: https://arxiv.org/abs/2505.05168 · HTML: https://mlsanity.com/paper/2505.05168/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 30 references that are in the map.
- First posted on arXiv 8 May 2025.

## Builds on (most cited first, 1 of 1)

- [Fr'echet Regression for Random Objects with Euclidean Predictors](https://mlsanity.com/paper/1608.03012/) (2016)

## Abstract (arXiv)

Under mild conditions, a least-squares local linear Fr'echet curve predictor is derived for a response and a regressor evaluated in a separable Hilbert space. The conditions that allow the implementation of the local linear Fr'echet functional predictor in the ambient L2-space of vector functions, with values in the time-varying tangent space of a compact Riemannian manifold, are established. An intrinsic local linear Fr'echet curve predictor on such a manifold is then proposed, based on a weighted Fr'echet mean approach. Its asymptotic optimality is proved. Simulations and a real-data application are considered to analyze the finite-sample performance of the empirical versions of both predictors, compared with a geodesic Nadaraya-Watson-type curve predictor. In the real-data application, the functional prediction of the time-varying spherical coordinates of the Earth's magnetic field is addressed usingobservations through time of the geocentric latitude and longitude of the NASA MAGSAT spacecraft.