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On Confidence Estimation Based on Quantitative Similarity Coefficients

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Abstract

We consider the problem of estimating the accuracy of quantitative similarity coefficients. For this purpose, we introduce a new concept of the similarity measure for the corresponding coefficient. We show that only frequency forms of quantitative similarity coefficients represent consistent estimates of their similarity measures. We obtain asymptotic confidence intervals for the RužiŽka and Bray-Curtis similarity measures based on the coefficients with the same names. We also propose a test for homogeneity of two populations based on the above-mentioned coefficients.

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Acknowledgments

The work of I.V. Rodionov in Sections 1 and 2 was supported by the Russian Science Foundation, project no. 19-11-00290 provided by the Steklov Mathematical Institute of the RAS.

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Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    I. V. Rodionov

  2. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

    I. V. Rodionov

  3. Institute of Plant and Animal Ecology, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russia

    A. N. Sozontov

Authors
  1. I. V. Rodionov
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  2. A. N. Sozontov
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Correspondence to I. V. Rodionov or A. N. Sozontov.

Additional information

This paper was recommended for publication by E.Ya. Rubinovich, a member of the Editorial Board

Russian Text © The Author(s), 2020, published in Avtomatika i Telemekhanika, 2020, No. 2, pp. 157–172.

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Rodionov, I.V., Sozontov, A.N. On Confidence Estimation Based on Quantitative Similarity Coefficients. Autom Remote Control 81, 320–332 (2020). https://doi.org/10.1134/S0005117920020101

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