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.

翻译：本文提出一类基于薄板（索伯列夫）惩罚的新型多元稳健平滑方法，特别适用于空间数据分析。所提出的估计量族可在高维情形下高效计算，具有坐标轴刚性变换不变性，并在温和假设条件下可证明具有最优理论性质。通过仿真实验及涉及臭氧浓度二维地理数据的实际案例，验证了所提出的薄板样条估计量相较于非稳健估计量的竞争性表现。