# Robust thin-plate splines for multivariate spatial smoothing

arXiv: https://arxiv.org/abs/2207.13931 · HTML: https://mlsanity.com/paper/2207.13931/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jul 2022.

## Built on by (most cited first, 1 of 1)

- [Representation Learning for Semiparametric Causal Mediation Analysis under No Essential Heterogeneity](https://mlsanity.com/paper/2607.10540/) (2026)

## Abstract (arXiv)

We propose a novel family of multivariate robust smoothers based on the thin-plate (Sobolev) penalty that is particularly suitable for the analysis of spatial data. The proposed family of estimators can be expediently computed even in high dimensions, is invariant with respect to rigid transformations of the coordinate axes and can be shown to possess optimal theoretical properties under mild assumptions. The competitive performance of the proposed thin-plate spline estimators relative to its non-robust counterpart is illustrated in a simulation study and a real data example involving two-dimensional geographical data on ozone concentration.