IDEAS home Printed from https://ideas.repec.org/a/gam/jijerp/v13y2016i10p953-d79119.html
   My bibliography  Save this article

Empirical Likelihood-Based ANOVA for Trimmed Means

Author

Listed:
  • Mara Velina

    (Department of Mathematics, Faculty of Physics and Mathematics, University of Latvia, Riga LV-1002, Latvia)

  • Janis Valeinis

    (Department of Mathematics, Faculty of Physics and Mathematics, University of Latvia, Riga LV-1002, Latvia)

  • Luca Greco

    (Department of Law, Economics, Management and Quantitative Methods, University of Sannio, Benevento 82100, Italy)

  • George Luta

    (Department of Biostatistics, Bioinformatics and Biomathematics, Georgetown University, Washington, DC 20057, USA)

Abstract

In this paper, we introduce an alternative to Yuen’s test for the comparison of several population trimmed means. This nonparametric ANOVA type test is based on the empirical likelihood (EL) approach and extends the results for one population trimmed mean from Qin and Tsao (2002). The results of our simulation study indicate that for skewed distributions, with and without variance heterogeneity, Yuen’s test performs better than the new EL ANOVA test for trimmed means with respect to control over the probability of a type I error. This finding is in contrast with our simulation results for the comparison of means, where the EL ANOVA test for means performs better than Welch’s heteroscedastic F test. The analysis of a real data example illustrates the use of Yuen’s test and the new EL ANOVA test for trimmed means for different trimming levels. Based on the results of our study, we recommend the use of Yuen’s test for situations involving the comparison of population trimmed means between groups of interest.

Suggested Citation

  • Mara Velina & Janis Valeinis & Luca Greco & George Luta, 2016. "Empirical Likelihood-Based ANOVA for Trimmed Means," IJERPH, MDPI, vol. 13(10), pages 1-13, September.
    • Handle: RePEc:gam:jijerp:v:13:y:2016:i:10:p:953-:d:79119
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1660-4601/13/10/953/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1660-4601/13/10/953/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Todorov, Valentin & Filzmoser, Peter, 2009. "An Object-Oriented Framework for Robust Multivariate Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i03).
    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. Steffen Liebscher & Thomas Kirschstein, 2015. "Efficiency of the pMST and RDELA location and scatter estimators," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 63-82, January.
    2. Torti, Francesca & Corbellini, Aldo & Atkinson, Anthony C., 2021. "fsdaSAS: a package for robust regression for very large datasets including the batch forward search," LSE Research Online Documents on Economics 109895, London School of Economics and Political Science, LSE Library.
    3. Alashwali, Fatimah & Kent, John T., 2016. "The use of a common location measure in the invariant coordinate selection and projection pursuit," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 145-161.
    4. B. Barış Alkan, 2016. "Robust Principal Component Analysis Based on Modified Minimum Covariance Determinant in the Presence of Outliers," Alphanumeric Journal, Bahadir Fatih Yildirim, vol. 4(2), pages 85-94, September.
    5. M. Hubert & P. Rousseeuw & K. Vakili, 2014. "Shape bias of robust covariance estimators: an empirical study," Statistical Papers, Springer, vol. 55(1), pages 15-28, February.
    6. Marco Riani & Andrea Cerioli & Francesca Torti, 2014. "On consistency factors and efficiency of robust S-estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 356-387, June.
    7. Matthias Kohl & Peter Ruckdeschel & Helmut Rieder, 2010. "Infinitesimally Robust estimation in general smoothly parametrized models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(3), pages 333-354, August.
    8. Bilodeau, Martin & Micheaux, Pierre Lafaye de & Mahdi, Smail, 2015. "The R Package groc for Generalized Regression on Orthogonal Components," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 65(i01).
    9. Gianna S. Monti & Peter Filzmoser & Roland C. Deutsch, 2018. "A Robust Approach to Risk Assessment Based on Species Sensitivity Distributions," Risk Analysis, John Wiley & Sons, vol. 38(10), pages 2073-2086, October.
    10. Sanjeena Subedi & Paul McNicholas, 2014. "Variational Bayes approximations for clustering via mixtures of normal inverse Gaussian distributions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(2), pages 167-193, June.
    11. T. Kirschstein & Steffen Liebscher, 2019. "Assessing the market values of soccer players – a robust analysis of data from German 1. and 2. Bundesliga," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(7), pages 1336-1349, May.
    12. Rafael Laboissière & Pierre-Alain Barraud & Corinne Cian, 2017. "Real and visually-induced body inclination differently affect the perception of object stability," PLOS ONE, Public Library of Science, vol. 12(10), pages 1-15, October.
    13. Baty, Florent & Ritz, Christian & Charles, Sandrine & Brutsche, Martin & Flandrois, Jean-Pierre & Delignette-Muller, Marie-Laure, 2015. "A Toolbox for Nonlinear Regression in R: The Package nlstools," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 66(i05).
    14. Vilijandas Bagdonavičius & Linas Petkevičius, 2020. "A new multiple outliers identification method in linear regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(3), pages 275-296, April.
    15. Jan Kalina & Jan Tichavský, 2022. "The minimum weighted covariance determinant estimator for high-dimensional data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(4), pages 977-999, December.
    16. Morris, Katherine & McNicholas, Paul D., 2016. "Clustering, classification, discriminant analysis, and dimension reduction via generalized hyperbolic mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 133-150.
    17. Andrea Bergesio & María Eugenia Szretter Noste & Víctor J. Yohai, 2021. "A robust proposal of estimation for the sufficient dimension reduction problem," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 758-783, September.
    18. Francesca Torti & Aldo Corbellini & Anthony C. Atkinson, 2021. "fsdaSAS: A Package for Robust Regression for Very Large Datasets Including the Batch Forward Search," Stats, MDPI, vol. 4(2), pages 1-21, April.
    19. Robert Finger, 2010. "Review of ‘Robustbase’ software for R," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(7), pages 1205-1210, November/.
    20. Selcuk Korkmaz & Gokmen Zararsiz & Dincer Goksuluk, 2015. "MLViS: A Web Tool for Machine Learning-Based Virtual Screening in Early-Phase of Drug Discovery and Development," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-15, April.

    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:gam:jijerp:v:13:y:2016:i:10:p:953-:d:79119. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.