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Testing against ordered alternatives in one-way ANOVA model with exponential errors

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Abstract

In this paper, a one-way heteroscedastic ANOVA model is considered with exponentially distributed errors. The likelihood ratio test (LRT) and two multiple comparison tests are developed for testing against ordered alternatives. A parametric bootstrap (PB) approach is proposed for implementation of tests and its asymptotic accuracy is proved. An extensive simulation study shows that all the proposed tests are accurate in terms of achieving the nominal size value, even for small samples. The proposed simultaneous confidence intervals are also seen to maintain the preassigned coverage probability. The powers of these tests are compared with a recently proposed test, which is quite conservative. Finally, the proposed tests are illustrated with the help of three data sets related to medical studies. We have developed an ‘R’ package for implementing our test procedures and shared it on the open platform ‘GitHub.’

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Acknowledgements

The authors are sincerely thankful to editor-in-chief, associate editor and two reviewers for their significant suggestions which have helped in improving the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721032, India

    Anjana Mondal & Somesh Kumar

  2. Department of Statistics, TU Dortmund University, 44227, Dortmund, Germany

    Markus Pauly

  3. Research Center Trustworthy Data Science and Security, UA Ruhr, 44227, Dortmund, Germany

    Markus Pauly

Authors
  1. Anjana Mondal
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  2. Markus Pauly
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  3. Somesh Kumar
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Correspondence to Somesh Kumar.

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Mondal, A., Pauly, M. & Kumar, S. Testing against ordered alternatives in one-way ANOVA model with exponential errors. Ann Inst Stat Math (2024). https://doi.org/10.1007/s10463-024-00897-7

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