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Chi-Squared Goodness-of-Fit Tests: The Optimal Choice of Grouping Intervals

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Recent Advances in Systems, Control and Information Technology (SCIT 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 543))

Abstract

When using the chi-squared goodness-of-fit tests, the problem of choosing boundary points and the number of grouping intervals is always urgent, as the power of these tests considerably depends on the grouping method used. In this paper, the investigation of the power of the Pearson and Nikulin-Rao-Robson chi-squared tests has been carried out for various numbers of intervals and grouping methods. The partition of the real line into equiprobable intervals is not an optimal grouping method, as a rule. It has been shown that asymptotically optimal grouping, for which the loss of the Fisher information from grouping is minimized, enables to maximize the power of the Pearson test against close competing hypotheses. In order to find the asymptotically optimal boundary points, it is possible to maximize some functional (the determinant, the trace or the minimum eigenvalue) of the Fisher information matrix for grouped data. The versions of asymptotically optimal grouping method maximize the test power relative to a set of close competing hypotheses, but they do not insure the largest power against some given competing hypothesis. For the given competing hypothesis H 1, it is possible to construct the chi-squared test, which has the largest power for testing hypothesis H 0 against H 1. For example, in the case of the Pearson chi-squared test, it is possible to maximize the non-centrality parameter for the given number of intervals. So, the purpose of this paper is to give the methods for the choice of optimal grouping intervals for chi-squared goodness-of-fit tests.

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Authors and Affiliations

  1. Novosibirsk State Technical University, Novosibirsk, Russia

    Ekaterina V. Chimitova & Boris Yu. Lemeshko

Authors
  1. Ekaterina V. Chimitova
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  2. Boris Yu. Lemeshko
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Correspondence to Ekaterina V. Chimitova .

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Editors and Affiliations

  1. Industrial Research Institute Automation and Measurements PIAP, Warsaw, Poland

    Roman Szewczyk

  2. Industrial Research Institute for Automation and Measurements PIAP, Warsaw, Poland

    Małgorzata Kaliczyńska

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Chimitova, E.V., Lemeshko, B.Y. (2017). Chi-Squared Goodness-of-Fit Tests: The Optimal Choice of Grouping Intervals. In: Szewczyk, R., Kaliczyńska, M. (eds) Recent Advances in Systems, Control and Information Technology. SCIT 2016. Advances in Intelligent Systems and Computing, vol 543. Springer, Cham. https://doi.org/10.1007/978-3-319-48923-0_82

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  • DOI: https://doi.org/10.1007/978-3-319-48923-0_82

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-48922-3

  • Online ISBN: 978-3-319-48923-0

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