This article is cited in 6 papers

Statistical Estimation of Generalized Dimensions

V. V. Maiorov, E. A. Timofeev

P. G. Demidov Yaroslavl State University

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.

UDC: 517.987

Received: 16.06.2000

DOI: 10.4213/mzm378

 English version: Mathematical Notes, 2002, 71:5, 634–648

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