IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v76y2024i4d10.1007_s10463-024-00897-7.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-024-00897-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10463-024-00897-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. Smaga, Łukasz, 2015. "Wald-type statistics using {2}-inverses for hypothesis testing in general factorial designs," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 215-220.
    3. Dickhaus, Thorsten & Sirotko-Sibirskaya, Natalia, 2019. "Simultaneous statistical inference in dynamic factor models: Chi-square approximation and model-based bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 129(C), pages 30-46.
    4. H. V. Kulkarni & S. M. Patil, 2021. "Uniformly implementable small sample integrated likelihood ratio test for one-way and two-way ANOVA under heteroscedasticity and normality," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(2), pages 273-305, June.
    5. Friedrich, Sarah & Brunner, Edgar & Pauly, Markus, 2017. "Permuting longitudinal data in spite of the dependencies," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 255-265.
    6. Stefano Bonnini & Getnet Melak Assegie & Kamila Trzcinska, 2024. "Review about the Permutation Approach in Hypothesis Testing," Mathematics, MDPI, vol. 12(17), pages 1-29, August.
    7. Baumeister, Marléne & Ditzhaus, Marc & Pauly, Markus, 2024. "Quantile-based MANOVA: A new tool for inferring multivariate data in factorial designs," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    8. Marc Ditzhaus & Roland Fried & Markus Pauly, 2021. "QANOVA: quantile-based permutation methods for general factorial designs," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 960-979, December.
    9. Markus Pauly & Maria Umlauft & Ali Ünlü, 2018. "Resampling-Based Inference Methods for Comparing Two Coefficients Alpha," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 203-222, March.
    10. Mondal, Anjana & Kumar, Somesh, 2024. "Inference on order restricted means of inverse Gaussian populations under heteroscedasticity," Computational Statistics & Data Analysis, Elsevier, vol. 194(C).
    11. Friedrich, Sarah & Pauly, Markus, 2018. "MATS: Inference for potentially singular and heteroscedastic MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 166-179.
    12. Marinho Bertanha & Eunyi Chung, 2023. "Permutation Tests at Nonparametric Rates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(544), pages 2833-2846, October.
    13. Hasler Mario, 2013. "Multiple Contrasts for Repeated Measures," The International Journal of Biostatistics, De Gruyter, vol. 9(1), pages 49-61, July.
    14. Mario Hasler, 2016. "Heteroscedasticity: multiple degrees of freedom vs. sandwich estimation," Statistical Papers, Springer, vol. 57(1), pages 55-68, March.
    15. Hothorn Ludwig A & Sill Martin & Schaarschmidt Frank, 2010. "Evaluation of Incidence Rates in Pre-Clinical Studies Using a Williams-Type Procedure," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-19, April.
    16. Philip Pallmann & Ludwig Hothorn & Gemechis Djira, 2014. "A Levene-type test of homogeneity of variances against ordered alternatives," Computational Statistics, Springer, vol. 29(6), pages 1593-1608, December.
    17. Meng Yuan & Chunlin Wang & Boxi Lin & Pengfei Li, 2022. "Semiparametric inference on general functionals of two semicontinuous populations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(3), pages 451-472, June.
    18. Chung, EunYi & Romano, Joseph P., 2016. "Multivariate and multiple permutation tests," Journal of Econometrics, Elsevier, vol. 193(1), pages 76-91.
    19. Dennis Dobler & Markus Pauly, 2018. "Bootstrap- and permutation-based inference for the Mann–Whitney effect for right-censored and tied data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 639-658, September.
    20. Wang, Chunlin & Marriott, Paul & Li, Pengfei, 2017. "Testing homogeneity for multiple nonnegative distributions with excess zero observations," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 146-157.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:aistmt:v:76:y:2024:i:4:d:10.1007_s10463-024-00897-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.