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.
Approximating distribution functions by iterated function systems / S.M. Iacus, D. La Torre. - In: JOURNAL OF APPLIED MATHEMATICS & DECISION SCIENCES. - ISSN 1173-9126. - 2005:1(2005), pp. 33-46. [10.1155/JAMDS.2005.33]
Approximating distribution functions by iterated function systems
S.M. IacusPrimo
;D. La TorreUltimo
2005
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.
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