Finite Element Thin Plate Splines in Density Estimation
by
Giles Hooker
Department of Mathematics, Australian National University

The problem of density estimation differs significantly from that of spline interpolation and for this reason has traditionally been dealt with by substancially different methods. We demonstrate that it is possible to apply thin plate spline-type functionals in the context of producing density functions for large data sets. The resulting estimators can be regarded as essentially kernel methods but may be applied to a broader range of problems. This approach also allows us to employ the finite element method, giving us access to automated prodeedures for selecting smoothing parameters and allowing us to obtain a potential computational saving.

Date received: July 29, 1999