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

Author

Listed:
  • Anjana Mondal

    (Indian Institute of Technology Kharagpur)

  • Markus Pauly

    (TU Dortmund University
    UA Ruhr)

  • Somesh Kumar

    (Indian Institute of Technology Kharagpur)

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.’

Suggested Citation

  • Anjana Mondal & Markus Pauly & Somesh Kumar, 2024. "Testing against ordered alternatives in one-way ANOVA model with exponential errors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(4), pages 649-678, August.
    • Handle: RePEc:spr:aistmt:v:76:y:2024:i:4:d:10.1007_s10463-024-00897-7
    DOI: 10.1007/s10463-024-00897-7
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    References listed on IDEAS

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    1. G. Vijayasree & Neeraj Misra & Harshinder Singh, 1995. "Componentwise estimation of ordered parameters ofk (≥2) exponential populations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(2), pages 287-307, June.
    2. Markus Pauly & Edgar Brunner & Frank Konietschke, 2015. "Asymptotic permutation tests in general factorial designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 461-473, March.
    3. Mondal, Anjana & Sattler, Paavo & Kumar, Somesh, 2023. "Testing against ordered alternatives in a two-way model without interaction under heteroscedasticity," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    4. Singh, Parminder & Singh, Navdeep, 2013. "Simultaneous confidence intervals for ordered pairwise differences of exponential location parameters under heteroscedasticity," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2673-2678.
    5. Bretz, Frank, 2006. "An extension of the Williams trend test to general unbalanced linear models," Computational Statistics & Data Analysis, Elsevier, vol. 50(7), pages 1735-1748, April.
    6. Maurya, Vishal & Goyal, Anju & Gill, Amar Nath, 2011. "Simultaneous testing for the successive differences of exponential location parameters under heteroscedasticity," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1507-1517, October.
    7. Konietschke, Frank & Bathke, Arne C. & Harrar, Solomon W. & Pauly, Markus, 2015. "Parametric and nonparametric bootstrap methods for general MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 291-301.
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