The link between kriging and thin-plate splines. (English) Zbl 0861.41006

Kent, J. T.; Mardia, K. V.

Kelly, F. P. (ed.), Probability, statistics and optimisation. A tribute to Peter Whittle. Chichester: Wiley. Wiley Series in Probability and Mathematical Statistics. Probability and Mathematical Statistics. 325-339 (1994).

From the authors’ introduction: “Kriging and thin-plate splines are two methods used for interpolating real-valued data as a function of a multivariable site. Under certain conditions it is well known that these two methods are equivalent to one another. The purpose of this paper is to give a self-contained and elementary description of the links between these two methods. The key tools for giving a unified explanation are of focus on self-similar random fields and the extensive use of Fourier methods. The main novelty of this paper is to attempt to pull together results from the scattered literature in a more comprehensible fashion. In addition the distinction between the order \(r\) of the polynomial drift and the intrinsic order \(p\) is emphasised, especially in \(d\geq 3\) dimensions”.
For the entire collection see [Zbl 0846.00009].

Reviewer: M.Lenard (Kuwait)

MSC:

41A15	Spline approximation
41A63	Multidimensional problems
65D05	Numerical interpolation
65D10	Numerical smoothing, curve fitting
62N99	Survival analysis and censored data

Keywords:

smoothing splines; intrinsic random fields; geostatistics; kriging; thin-plate splines; self-similar random fields