Robust thin-plate splines for multivariate spatial smoothing

TL;DR

This paper introduces a new family of robust multivariate thin-plate spline smoothers for spatial data analysis, offering computational efficiency, invariance properties, and strong theoretical guarantees, demonstrated through simulations and real-world ozone data.

Contribution

It presents a novel robust multivariate smoothing method based on thin-plate splines with optimal theoretical properties and practical advantages in high-dimensional spatial data analysis.

Findings

Robust estimators perform well in simulations.

Method is invariant under rigid transformations.

Effective on real geographical ozone data.

Abstract

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.