IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v67y2013icp175-184.html
   My bibliography  Save this article

Combining functions and the closure principle for performing follow-up tests in functional analysis of variance

Author

Listed:
  • Vsevolozhskaya, O.A.
  • Greenwood, M.C.
  • Bellante, G.J.
  • Powell, S.L.
  • Lawrence, R.L.
  • Repasky, K.S.

Abstract

Functional analysis of variance involves testing for differences in functional means across k groups in n functional responses. If a significant overall difference in the mean curves is detected, one may want to identify the location of these differences. Cox and Lee (2008) proposed performing a point-wise test and applying the Westfall–Young multiple comparison correction. We propose an alternative procedure for identifying regions of significant difference in the functional domain. Our procedure is based on a region-wise test and application of a combining function along with the closure multiplicity adjustment principle. We give an explicit formulation of how to implement our method and show that it performs well in a simulation study. The use of the new method is illustrated with an analysis of spectral responses related to vegetation changes from a CO2 release experiment.

Suggested Citation

  • Vsevolozhskaya, O.A. & Greenwood, M.C. & Bellante, G.J. & Powell, S.L. & Lawrence, R.L. & Repasky, K.S., 2013. "Combining functions and the closure principle for performing follow-up tests in functional analysis of variance," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 175-184.
    • Handle: RePEc:eee:csdana:v:67:y:2013:i:c:p:175-184
    DOI: 10.1016/j.csda.2013.05.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947313001667
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2013.05.005?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. J. C. Gower & W. J. Krzanowski, 1999. "Analysis of distance for structured multivariate data and extensions to multivariate analysis of variance," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(4), pages 505-519.
    2. Dennis D. Cox & Jong Soo Lee, 2008. "Pointwise testing with functional data using the Westfall--Young randomization method," Biometrika, Biometrika Trust, vol. 95(3), pages 621-634.
    3. Pedro Delicado, 2007. "Functional k-sample problem when data are density functions," Computational Statistics, Springer, vol. 22(3), pages 391-410, September.
    4. Cuevas, Antonio & Febrero, Manuel & Fraiman, Ricardo, 2004. "An anova test for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 111-122, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pini, Alessia & Sørensen, Helle & Tolver, Anders & Vantini, Simone, 2023. "Local inference for functional linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).

    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. Łukasz Smaga & Jin‐Ting Zhang, 2020. "Linear hypothesis testing for weighted functional data with applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(2), pages 493-515, June.
    2. Matthias Studer & Gilbert Ritschard & Alexis Gabadinho & Nicolas S. Müller, 2011. "Discrepancy Analysis of State Sequences," Sociological Methods & Research, , vol. 40(3), pages 471-510, August.
    3. Dalia Valencia & Rosa E. Lillo & Juan Romo, 2019. "A Kendall correlation coefficient between functional 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. 13(4), pages 1083-1103, December.
    4. Zhang, Jin-Ting & Cheng, Ming-Yen & Wu, Hau-Tieng & Zhou, Bu, 2019. "A new test for functional one-way ANOVA with applications to ischemic heart screening," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 3-17.
    5. Pini, Alessia & Stamm, Aymeric & Vantini, Simone, 2018. "Hotelling’s T2 in separable Hilbert spaces," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 284-305.
    6. Valencia García, Dalia Jazmin & Lillo Rodríguez, Rosa Elvira & Romo, Juan, 2013. "A Kendall correlation coefficient for functional dependence," DES - Working Papers. Statistics and Econometrics. WS ws133228, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Łukasz Smaga, 2020. "A note on repeated measures analysis for functional data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 117-139, March.
    8. Martínez-Camblor, Pablo & Corral, Norberto, 2011. "Repeated measures analysis for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3244-3256, December.
    9. Christian Acal & Ana M. Aguilera, 2023. "Basis expansion approaches for functional analysis of variance with repeated measures," 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. 17(2), pages 291-321, June.
    10. Qiu, Zhiping & Chen, Jianwei & Zhang, Jin-Ting, 2021. "Two-sample tests for multivariate functional data with applications," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    11. Livio Corain & Viatcheslav Melas & Andrey Pepelyshev & Luigi Salmaso, 2014. "New insights on permutation approach for hypothesis testing on functional 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. 8(3), pages 339-356, September.
    12. Pini, Alessia & Spreafico, Lorenzo & Vantini, Simone & Vietti, Alessandro, 2019. "Multi-aspect local inference for functional data: Analysis of ultrasound tongue profiles," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 162-185.
    13. A. Pini & S. Vantini, 2017. "Interval-wise testing for functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(2), pages 407-424, April.
    14. István Berkes & Robertas Gabrys & Lajos Horváth & Piotr Kokoszka, 2009. "Detecting changes in the mean of functional observations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 927-946, November.
    15. Ana-Maria Staicu & Yingxing Li & Ciprian M. Crainiceanu & David Ruppert, 2014. "Likelihood Ratio Tests for Dependent Data with Applications to Longitudinal and Functional Data Analysis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 932-949, December.
    16. Yin, Xu & Wang, Jing & Li, Yurui & Feng, Zhiming & Wang, Qianyi, 2021. "Are small towns really inefficient? A data envelopment analysis of sampled towns in Jiangsu province, China," Land Use Policy, Elsevier, vol. 109(C).
    17. Konrad Abramowicz & Alessia Pini & Lina Schelin & Sara Sjöstedt de Luna & Aymeric Stamm & Simone Vantini, 2023. "Domain selection and familywise error rate for functional data: A unified framework," Biometrics, The International Biometric Society, vol. 79(2), pages 1119-1132, June.
    18. Joseph, Esdras & Galeano San Miguel, Pedro & Lillo Rodríguez, Rosa Elvira, 2015. "Two-sample Hotelling's T² statistics based on the functional Mahalanobis semi-distance," DES - Working Papers. Statistics and Econometrics. WS ws1503, Universidad Carlos III de Madrid. Departamento de Estadística.
    19. Flores Díaz, Ramón Jesús & Lillo Rodríguez, Rosa Elvira & Romo, Juan, 2014. "Homogeneity test for functional data based on depth measures," DES - Working Papers. Statistics and Econometrics. WS ws140101, Universidad Carlos III de Madrid. Departamento de Estadística.
    20. Balogoun, Armando Sosthène Kali & Nkiet, Guy Martial & Ogouyandjou, Carlos, 2021. "Asymptotic normality of a generalized maximum mean discrepancy estimator," Statistics & Probability Letters, Elsevier, vol. 169(C).

    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:eee:csdana:v:67:y:2013:i:c:p:175-184. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.