Mathematical Notes

, Volume 71, Issue 5, pp 634–648

Statistical Estimation of Generalized Dimensions

  • V. V. Maiorov
  • E. A. Timofeev
Article

DOI: 10.1023/A:1015883820677

Cite this article as:
Maiorov, V.V. & Timofeev, E.A. Mathematical Notes (2002) 71: 634. doi:10.1023/A:1015883820677

Abstract

A statistical estimate for generalized dimensions of a set \(A \subset \mathbb{R}^m\) based on the computation of average distances to the closest points in a sample of elements of A is given. For smooth manifolds with Lebesgue measures and for self-similar fractals with self-similar measures, the estimate is proved to be consistent.

generalized dimensions Rényi dimensions consistent estimates smooth manifolds self-similar fractals random points 

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • V. V. Maiorov
    • 1
  • E. A. Timofeev
    • 1
  1. 1.Yaroslavl State UniversityRussia

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