On Fractal Distribution Function Estimation and Applications

UNIMI Economics Working Paper No. 07.2002

30 Pages Posted: 21 Nov 2004

See all articles by Stefano Maria Iacus

Stefano Maria Iacus

University of Milan - Department of Economics, Business and Statistics

Davide La Torre

SKEMA Business School

Date Written: March 2002

Abstract

In this paper we review some recent results concerning the approximations of distribution functions and measures on [0,1] based on iterated function systems. The two different approaches available in the literature are considered and their relation are investigated in the statistical perspective. In the second part of the paper we propose a new class of estimators for the distribution function and the related characteristic and density functions. Glivenko-Cantelli, LIL properties and local asymptotic minimax efficiency are established for some of the proposed estimators. Via Monte Carlo analysis we show that, for small sample sizes, the proposed estimator can be as efficient or even better than the empirical distribution function and the kernel density estimator respectively. This paper is to be considered as a first attempt in the construction of new class of estimators based on fractal objects. Pontential applications to survival analysis with random censoring are proposed at the end of the paper.

Keywords: Fractals, estimation

JEL Classification: C13, C63

Suggested Citation

Iacus, Stefano Maria and La Torre, Davide, On Fractal Distribution Function Estimation and Applications (March 2002). UNIMI Economics Working Paper No. 07.2002, Available at SSRN: https://ssrn.com/abstract=616623 or http://dx.doi.org/10.2139/ssrn.616623

Stefano Maria Iacus

University of Milan - Department of Economics, Business and Statistics ( email )

Via Conservatorio 7
Milano, 20122
Italy
+390250321461 (Phone)
+3950321505 (Fax)

HOME PAGE: http://www.economia.unimi.it/iacus

Davide La Torre (Contact Author)

SKEMA Business School ( email )

Sophia Antipolis
France

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