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Matematicheskie Zametki, 2002, Volume 71, Issue 5, Pages 697–712
DOI: https://doi.org/10.4213/mzm378 (Mi mzm378) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Statistical Estimation of Generalized Dimensions

V. V. Maiorov, E. A. Timofeev

P. G. Demidov Yaroslavl State University
Full-text PDF (255 kB) Citations (6)
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DOI: https://doi.org/10.4213/mzm378
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.
Received: 16.06.2000
English version:
Mathematical Notes, 2002, Volume 71, Issue 5, Pages 634–648
DOI: https://doi.org/10.1023/A:1015883820677
Bibliographic databases:
UDC: 517.987
Language: Russian
Citation: V. V. Maiorov, E. A. Timofeev, “Statistical Estimation of Generalized Dimensions”, Mat. Zametki, 71:5 (2002), 697–712; Math. Notes, 71:5 (2002), 634–648
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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