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Mat. Zametki, 2002, Volume 71, Issue 5, Pages 697–712 (Mi mz378)  

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

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.

DOI: https://doi.org/10.4213/mzm378

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

Bibliographic databases:

UDC: 517.987
Received: 16.06.2000

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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\paper Statistical Estimation of Generalized Dimensions
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. A. Timofeev, “A Consistent Estimator of the Entropy of Measures and Dynamical Systems”, Math. Notes, 77:6 (2005), 831–842  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. E. A. Timofeev, “Invariants of measures admiting statistical estimates”, St. Petersburg Math. J., 17:3 (2006), 527–551  mathnet  crossref  mathscinet  zmath  elib
    3. N. E. Timofeeva, “Ekonomnyi algoritm nakhozhdeniya srednikh minimalnykh rasstoyanii”, Model. i analiz inform. sistem, 14:3 (2007), 50–52  mathnet
    4. Kaltchenko A., Yang E.-h., Tirnofeeva N., “Entropy Estimators with Almost Sure Convergence and an O(N(-1)) Variance”, 2007 IEEE Information Theory Workshop, Vols 1 and 2, IEEE, 2007, 644–649  crossref  isi  scopus
    5. Kaltchenko, A, “Entropy estimators with almost sure convergence and an $\scr O(n\sp {-1})$ variance”, Advances in Mathematics of Communications, 2:1 (2008), 1-13  crossref  mathscinet  zmath  isi  scopus
    6. Kaltchenko A., “Estimation of Classical and Quantum Entropy and Other Information-Theoretic Quantities - Art. No. 69760l”, Quantum Information and Computation VI, Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), 6976, eds. Donkor E., Pirich A., Brandt H., SPIE-Int Soc Optical Engineering, 2008, L9760  crossref  isi  scopus
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