Finite element thin plate splines in density estimation
Markus Hegland, Giles Hooker and Stephen Roberts
(Received 7 August 2000)
Abstract
The problem of estimating probability density functions differs
significantly from functional estimation in which a response variable
is present and has for this reason has been dealt with by
substantially different methods. We demonstrate here that it is
possible to apply spline-type functionals to the problem of density
estimation for large data sets. The resulting estimators may be
regarded as kernel methods, but may also be applied to inexact or
aggregated data. They can be seen to have moments matching the
empirical moments of the data up to the degree of smoothness of the
function. Finally, we will show that these functions may be naturally
approximated by a finite element method and that doing so will make
the method scalable.