IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v39y2024i2d10.1007_s00180-022-01298-1.html
   My bibliography  Save this article

Adaptive tests for ANOVA in Fisher–von Mises–Langevin populations under heteroscedasticity

Author

Listed:
  • Shreyashi Basak

    (Indian Institute of Technology Kharagpur)

  • Markus Pauly

    (TU Dortmund University
    UA Ruhr)

  • Somesh Kumar

    (Indian Institute of Technology Kharagpur)

Abstract

Fisher–von Mises–Langevin distributions are widely used for modeling directional data. In this paper, the problem of testing homogeneity of mean directions of several Fisher–von Mises–Langevin populations is considered when the concentration parameters are unknown and heterogeneous. First, an adaptive test based on the likelihood ratio statistic is proposed. Critical points are evaluated using a parametric bootstrap. Second, a heuristic test statistic is considered based on pairwise group differences. A nonparametric bootstrap procedure is adapted for evaluating critical points. Finally, a permutation test is also proposed. An extensive simulation study is performed to compare the size and power values of these tests with those proposed earlier. It is observed that both parametric and nonparametric bootstrap based tests achieve size values quite close to the nominal size. Asymptotic tests and permutation tests have size values higher than the nominal size. Bootstrap tests are seen to have very good power performance. The robustness of tests is also studied by considering contamination in Fisher–von Mises–Langevin distributions. R packages are developed for the actual implementation of all tests. A real data set has been considered for illustrations.

Suggested Citation

  • Shreyashi Basak & Markus Pauly & Somesh Kumar, 2024. "Adaptive tests for ANOVA in Fisher–von Mises–Langevin populations under heteroscedasticity," Computational Statistics, Springer, vol. 39(2), pages 433-459, April.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:2:d:10.1007_s00180-022-01298-1
    DOI: 10.1007/s00180-022-01298-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-022-01298-1
    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/s00180-022-01298-1?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. Christophe Ley & Yvik Swan & Thomas Verdebout, 2017. "Efficient ANOVA for directional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 39-62, February.
    2. 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.
    3. Feridun Tasdan & Ozgur Yeniay, 2018. "A comparative simulation of multiple testing procedures in circular data problems," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(2), pages 255-269, January.
    4. Hornik, Kurt & Grün, Bettina, 2014. "movMF: An R Package for Fitting Mixtures of von Mises-Fisher Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 58(i10).
    5. Adelaide Figueiredo, 2017. "Bootstrap and permutation tests in ANOVA for directional data," Computational Statistics, Springer, vol. 32(4), pages 1213-1240, December.
    6. E. N. Johnson & S. J. Richter, 2022. "Permutation tests for mixed paired and two-sample designs," Computational Statistics, Springer, vol. 37(2), pages 739-750, April.
    7. Arthur Pewsey & Eduardo García-Portugués, 2021. "Rejoinder on: Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 76-82, March.
    8. 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.
    9. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    10. Friedrich, Sarah & Pauly, Markus, 2018. "MATS: Inference for potentially singular and heteroscedastic MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 166-179.
    11. Chung, EunYi & Romano, Joseph P., 2016. "Multivariate and multiple permutation tests," Journal of Econometrics, Elsevier, vol. 193(1), pages 76-91.
    12. Amaral, G.J.A. & Dryden, I.L. & Wood, Andrew T.A., 2007. "Pivotal Bootstrap Methods for k-Sample Problems in Directional Statistics and Shape Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 695-707, June.
    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. Friedrich, Sarah & Pauly, Markus, 2018. "MATS: Inference for potentially singular and heteroscedastic MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 166-179.
    2. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    3. Zimmermann, Georg & Pauly, Markus & Bathke, Arne C., 2020. "Multivariate analysis of covariance with potentially singular covariance matrices and non-normal responses," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    4. Fernández de Marcos Giménez de los Galanes, Alberto & García Portugués, Eduardo, 2022. "Data-driven stabilizations of goodness-of-fit tests," DES - Working Papers. Statistics and Econometrics. WS 35324, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. Mardia, Kanti V. & Wiechers, Henrik & Eltzner, Benjamin & Huckemann, Stephan F., 2022. "Principal component analysis and clustering on manifolds," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    6. Alberto Fernández-de-Marcos & Eduardo García-Portugués, 2023. "On new omnibus tests of uniformity on the hypersphere," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(4), pages 1508-1529, December.
    7. 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.
    8. Fernández-de-Marcos, Alberto & García-Portugués, Eduardo, 2023. "Data-driven stabilizations of goodness-of-fit tests," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    9. Maxime Boucher & Andrea Meilán-Vila & Vivien Meurice & Thomas Verdebout, 2025. "On a modified Watson test for spherical location," Statistical Papers, Springer, vol. 66(4), pages 1-12, June.
    10. Welz, Thilo & Viechtbauer, Wolfgang & Pauly, Markus, 2023. "Cluster-robust estimators for multivariate mixed-effects meta-regression," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    11. Andrew Harvey & Dario Palumbo, 2023. "Regime switching models for circular and linear time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(4), pages 374-392, July.
    12. Harvey, Andrew & Hurn, Stan & Palumbo, Dario & Thiele, Stephen, 2024. "Modelling circular time series," Journal of Econometrics, Elsevier, vol. 239(1).
    13. Jeon, Jeong Min & Van Keilegom, Ingrid, 2023. "Density estimation for mixed Euclidean and non-Euclidean data in the presence of measurement error," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    14. Xu Qin & Huiqun Gao, 2024. "Nonparametric binary regression models with spherical predictors based on the random forests kernel," Computational Statistics, Springer, vol. 39(6), pages 3031-3048, September.
    15. William Bell & Saralees Nadarajah, 2024. "A Review of Wrapped Distributions for Circular Data," Mathematics, MDPI, vol. 12(16), pages 1-51, August.
    16. 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).
    17. Dennis Dobler & Sarah Friedrich & Markus Pauly, 2020. "Nonparametric MANOVA in meaningful effects," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 997-1022, August.
    18. Ludwig Baringhaus & Rudolf Grübel, 2024. "Discrete mixture representations of spherical distributions," Statistical Papers, Springer, vol. 65(2), pages 557-596, April.
    19. Andrade, Ana C.C. & Pereira, Gustavo H.A. & Artes, Rinaldo, 2023. "The circular quantile residual," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    20. Jeong Min Jeon & Ingrid Van Keilegom, 2024. "Density estimation and regression analysis on hyperspheres in the presence of measurement error," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(2), pages 513-556, June.

    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:compst:v:39:y:2024:i:2:d:10.1007_s00180-022-01298-1. 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.