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Statistical Estimation of Generalized Dimensions

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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.

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Authors and Affiliations

  1. Yaroslavl State University, Russia

    V. V. Maiorov & E. A. Timofeev

Authors
  1. V. V. Maiorov
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  2. E. A. Timofeev
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Maiorov, V.V., Timofeev, E.A. Statistical Estimation of Generalized Dimensions. Mathematical Notes 71, 634–648 (2002). https://doi.org/10.1023/A:1015883820677

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