Abstract
Recently, a spherical wavelet method was proposed by Li (SIAM J. Scientific Computing 1999; 21: 924-953) for multiscale representation and analysis of scattered spherical data. Practical implementation of the method requires (a) a multiscale spherical-basis-function (SBF) representation that extrapolates' the scattered data on the entire globe and (b) properly designed analysis networks and SBF bandwidths that ensure the stability of the SBF representation and an appropriate multiscale interpretation of the analysis. This paper discusses several statistical estimation methods for obtaining the SBF representation from scattered data. The paper also discusses an automatic procedure for network design and bandwidth selection. Cross-validation techniques are proposed for the determination of design parameters with the aim of balancing the goodness of fit and the stability of representation. The entire approach is illustrated and tested by an example of surface air temperature observed by a global network of weather stations.
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