Geographic Premium Rating by Whittaker- Spatial Smoothing

Whittaker graduation is applied to the spatial smoothing of insurance data. Such data (I.e. claim frequency) form a surface over the 2-dimensional geographic domain to which they relate. Observations of this surface are subject to sampling error. They need to be smoothed spatially if a reliable estimate of the underlying surface is to be obtained. A measure of smoothness of a surface has been defined. This has been incorporated in 2-dimensional Whittaker graduation to effect the necessary smoothing. The details of this are worked out in Section 4. The procedure is illustrated by numerical example in Section 5. The Bayesian interpretation of this form of spatial smoothing is discussed, and used to assist in the selection of the Whittaker relativity constant.