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Application of Nonparametric Goodness-of-Fit Tests for Composite Hypotheses in Case of Unknown Distributions of Statistics

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Topics in Statistical Simulation

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 114))

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Abstract

While testing composite hypotheses when a scalar or vector parameter of the probability distribution is calculated using the same sample, nonparametric Kolmogorov, Kuiper, Cramer–von Mises–Smirnov, Watson and Anderson–Darling goodness-of-fit tests lose their distribution freedom. When testing composite hypotheses conditional distribution of the test statistic depends on several factors, even the specific values of the distribution shape parameters. An interactive method for investigating distributions of nonparametric goodness-of-fit tests statistics, that allows us apply criteria for testing any composite hypotheses using a variety of estimation methods, is implemented.

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Acknowledgements

This research has been supported by the Russian Ministry of Education and Science (project 2.541.2014K).

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Authors and Affiliations

  1. Department of Applied Mathematics, Novosibirsk State Technical University, K. Marx pr., 20, Novosibirsk, Russia

    Boris Yu. Lemeshko, Alisa A. Gorbunova, Stanislav B. Lemeshko & Andrey P. Rogozhnikov

Authors
  1. Boris Yu. Lemeshko
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  2. Alisa A. Gorbunova
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  3. Stanislav B. Lemeshko
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  4. Andrey P. Rogozhnikov
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Corresponding author

Correspondence to Boris Yu. Lemeshko .

Editor information

Editors and Affiliations

  1. St.Petersburg State University, St.Petersburg, Russia

    V.B. Melas

  2. University of Bologna, Rimini, Italy

    Stefania Mignani

  3. University of Bologna, Rimini, Italy

    Paola Monari

  4. University of Padova, Padova, Italy

    Luigi Salmaso

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Lemeshko, B.Y., Gorbunova, A.A., Lemeshko, S.B., Rogozhnikov, A.P. (2014). Application of Nonparametric Goodness-of-Fit Tests for Composite Hypotheses in Case of Unknown Distributions of Statistics. In: Melas, V., Mignani, S., Monari, P., Salmaso, L. (eds) Topics in Statistical Simulation. Springer Proceedings in Mathematics & Statistics, vol 114. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2104-1_31

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