Advances in Decision Sciences
Volume 2005 (2005), Issue 1, Pages 33-46
doi:10.1155/JAMDS.2005.33
Approximating distribution functions by iterated function systems
Stefano Maria Iacus
and Davide La Torre
Department of Mathematics, University of Ulster, Ireland
Abstract
An iterated function system (IFS) on the space of distribution functions is built with the aim of proposing a new class of distribution function estimators. One IFS estimator and its asymptotic properties are studied in detail. We also propose a density estimator derived from the IFS distribution function estimator by using Fourier analysis. Relative efficiencies of both estimators, for small and moderate sample sizes, are presented via Monte Carlo analysis.