Riemannian Simultaneous Inference for Tangent Vector Field Regression
We consider nonparametric tangent vector field regression on a Riemannian manifold without boundary. Because responses at different points lie in different tangent spaces, the proposed kernel estimator first parallel transports nearby responses to the target tangent space and then forms a volume-corrected local average. We first derive its uniform second-order bias, finite-bandwidth covariance, and stochastic rate. For simultaneous inference, the tangent norm is written as a supremum over the unit tangent bundle. Exact covariance whitening gives a unit-variance Gaussian field whose correlation length is of order $h$ along the base manifold and of order one along the fibre. Its local covar...
| Authors | Xiaotian Chang, Yangdi Jiang, Qirui Hu |
|---|---|
| Primary category | stat.ML |
| Published | 18 September 2026 |
| Last updated at source | 22 September 2026 |
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