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.
Highlights
The iterated function systems (IFSs) were born in the mid eighties [2, 7] as applications of the theory of discrete dynamical systems and as useful tools for buildings’ fractals and other similar sets
Some possible applications of IFSs can be found in image processing theory [4], in the theory of stochastic growth models [14], and in the theory of random dynamical systems [1, 3, 9]
If one is able to solve the inverse problem exactly, it is possible to identify f with the operator T which has it as fixed point
Summary
The iterated function systems (IFSs) were born in the mid eighties [2, 7] as applications of the theory of discrete dynamical systems and as useful tools for buildings’ fractals and other similar sets. Some possible applications of IFSs can be found in image processing theory [4], in the theory of stochastic growth models [14], and in the theory of random dynamical systems [1, 3, 9]. We propose an IFS distribution function estimator and we study its properties. Monte Carlo analysis seems to show some gain of the IFS over the EDF
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