The Annals of Probability

Nearest-Neighbor Analysis of a Family of Fractal Distributions

Colleen D. Cutler and Donald A. Dawson

Full-text: Open access

Abstract

In this paper we use a central limit theorem for entropy due to Ibragimov to obtain limit theorems for linear normalizations of the log minimum distance when observations are sampled from measures belonging to a family of fractal distributions. It is shown that in almost all cases the limit distribution is Gaussian with parameters determined in part by the Hausdorff dimension associated with the underlying measure. Exceptions to this rule include absolutely continuous measures which obey the classical extreme value limit laws.

Article information

Source
Ann. Probab., Volume 18, Number 1 (1990), 256-271.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990948

Digital Object Identifier
doi:10.1214/aop/1176990948

Mathematical Reviews number (MathSciNet)
MR1043947

Zentralblatt MATH identifier
0715.60024

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 62E20: Asymptotic distribution theory

Keywords
Nearest neighbor Hausdorff dimension entropy fractal distribution dimension estimation extreme values

Citation

Cutler, Colleen D.; Dawson, Donald A. Nearest-Neighbor Analysis of a Family of Fractal Distributions. Ann. Probab. 18 (1990), no. 1, 256--271. doi:10.1214/aop/1176990948. https://projecteuclid.org/euclid.aop/1176990948


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