Multivariate spatial smoothing using additive regression splines

Abstract

We describe additive regression spline models as tools for smooth interpolation of fields that depend on several variables in a spatially varying way. Additive regression models can bypass the usual technical difficulties associated with the curse of dimension. We formulate the additive regression spline minimisation problem and prove that this problem is uniquely solvable under suitable conditions on the data. The resulting additive regression spline may be seen as a special case of general additive tensor product splines. Moreover, we show that additive regression splines may be implemented by a relatively straightforward extension of the methods used in the implementation of standard thin plate splines. The performance of additive regression splines is demonstrated on a simulated noisy data set.