Finite element thin plate splines in density estimation

Markus Hegland, Giles Hooker, Stephen Roberts

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.

Full Text:

PDF


DOI: http://dx.doi.org/10.21914/anziamj.v42i0.2232



Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.