Cross-Validation design of Matlab Spatial Smoothers

Bivariate (spatial) nonparametric interpolation techniques of Matlab such as Thin plate Spline (TPS) and Locally weighted smoothing (LWS) can estimate random surfaces on a lattice, from local point observations. The automatic selection of their smoothing coefficients (say 0<1) are performed by Matlab with ad-hoc numerical approaches, such as: a trade-off between data fitting and curve roughness (TPS) , or a heuristic percentage of neighboring data points (LWS). This function computes the optimal smoothing coefficients with Cross- Validation (CV) criteria (i.e. out-of-sample prediction of each data point) then estimate the required surface on a grid of equispaced nodes.