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Approximating distribution functions by iterated function systems. (English) Zbl 1094.62011
Summary: 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.

62E10 Characterization and structure theory of statistical distributions
62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
28A99 Classical measure theory
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