IDEAS home Printed from https://ideas.repec.org/p/cte/wsrepe/ws140101.html
   My bibliography  Save this paper

Homogeneity test for functional data based on depth measures

Author

Listed:
  • Flores Díaz, Ramón Jesús
  • Lillo Rodríguez, Rosa Elvira
  • Romo, Juan

Abstract

In the context of functional data analysis, we propose a new method to test the homogeneity of families of functions. Based on some well-known depth measures, we construct four different statistics in order to measure distance between the two families. A simulation study is performed to check the efficiency of the testswhen confronted with shape and magnitude perturbation. Finally, we apply these tools to measure the homogeneity in some families of real data, obtaining good results for these new methods.

Suggested Citation

  • 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.
    • Handle: RePEc:cte:wsrepe:ws140101
    as

    Download full text from publisher

    File URL: https://e-archivo.uc3m.es/rest/api/core/bitstreams/782d35e6-8cc4-44db-b014-149202f149b1/content
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. C. Abraham & P. A. Cornillon & E. Matzner‐Løber & N. Molinari, 2003. "Unsupervised Curve Clustering using B‐Splines," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(3), pages 581-595, September.
    2. Alonso, Andrés M. & Casado, David & Romo, Juan, 2012. "Supervised classification for functional data: A weighted distance approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2334-2346.
    3. 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.
    4. López-Pintado, Sara & Romo, Juan, 2009. "On the Concept of Depth for Functional Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 718-734.
    5. Amparo Baíllo & Antonio Cuevas & Juan Antonio Cuesta‐Albertos, 2011. "Supervised Classification for a Family of Gaussian Functional Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(3), pages 480-498, September.
    6. Cuevas, Antonio & Febrero, Manuel & Fraiman, Ricardo, 2006. "On the use of the bootstrap for estimating functions with functional data," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1063-1074, November.
    7. Antonio Cuevas & Manuel Febrero & Ricardo Fraiman, 2007. "Robust estimation and classification for functional data via projection-based depth notions," Computational Statistics, Springer, vol. 22(3), pages 481-496, September.
    8. Ricardo Fraiman & Graciela Muniz, 2001. "Trimmed means for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 419-440, December.
    9. Li, Bin & Yu, Qingzhao, 2008. "Classification of functional data: A segmentation approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4790-4800, 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. Mia Hubert & Peter Rousseeuw & Pieter Segaert, 2015. "Multivariate functional outlier detection," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 177-202, July.
    2. Carlo Sguera & Pedro Galeano & Rosa Lillo, 2014. "Spatial depth-based classification for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(4), pages 725-750, December.
    3. Nagy, Stanislav & Ferraty, Frédéric, 2019. "Data depth for measurable noisy random functions," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 95-114.
    4. Alba M. Franco-Pereira & Rosa E. Lillo, 2020. "Rank tests for functional data based on the epigraph, the hypograph and associated graphical representations," 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. 14(3), pages 651-676, September.
    5. López-Pintado, Sara & Romo, Juan, 2011. "A half-region depth for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1679-1695, April.
    6. Blanquero, R. & Carrizosa, E. & Jiménez-Cordero, A. & Martín-Barragán, B., 2019. "Functional-bandwidth kernel for Support Vector Machine with Functional Data: An alternating optimization algorithm," European Journal of Operational Research, Elsevier, vol. 275(1), pages 195-207.
    7. Joseph, Esdras & Galeano San Miguel, Pedro & Lillo Rodríguez, Rosa Elvira, 2013. "The Mahalanobis distance for functional data with applications to classification," DES - Working Papers. Statistics and Econometrics. WS ws131312, Universidad Carlos III de Madrid. Departamento de Estadística.
    8. Valencia García, Dalia Jazmin & Lillo Rodríguez, Rosa Elvira & Romo, Juan, 2013. "Spearman coefficient for functions," DES - Working Papers. Statistics and Econometrics. WS ws133329, Universidad Carlos III de Madrid. Departamento de Estadística.
    9. Olusola Samuel Makinde, 2019. "Classification rules based on distribution functions of functional depth," Statistical Papers, Springer, vol. 60(3), pages 629-640, June.
    10. Fabrizio Maturo & Francesca Fortuna & Tonio Di Battista, 2024. "Outliers detection in assessment tests’ quality evaluation through the blended use of functional data analysis and item response theory," Annals of Operations Research, Springer, vol. 342(3), pages 1547-1562, November.
    11. J. A. Cuesta-Albertos & M. Febrero-Bande & M. Oviedo de la Fuente, 2017. "The $$\hbox {DD}^G$$ DD G -classifier in the functional setting," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 119-142, March.
    12. Alonso, Andrés M. & Casado, David & Romo, Juan, 2012. "Supervised classification for functional data: A weighted distance approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2334-2346.
    13. Miguel Martínez Comesaña & Sandra Martínez Mariño & Pablo Eguía Oller & Enrique Granada Álvarez & Aitor Erkoreka González, 2020. "A Functional Data Analysis for Assessing the Impact of a Retrofitting in the Energy Performance of a Building," Mathematics, MDPI, vol. 8(4), pages 1-20, April.
    14. Jiménez Recaredo, Raúl José & Elías Fernández, Antonio, 2017. "Prediction Bands for Functional Data Based on Depth Measures," DES - Working Papers. Statistics and Econometrics. WS 24606, Universidad Carlos III de Madrid. Departamento de Estadística.
    15. Nieto-Reyes, Alicia & Battey, Heather, 2021. "A topologically valid construction of depth for functional data," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    16. Zhuo Qu & Wenlin Dai & Marc G. Genton, 2021. "Robust functional multivariate analysis of variance with environmental applications," Environmetrics, John Wiley & Sons, Ltd., vol. 32(1), February.
    17. Miguel Flores & Salvador Naya & Rubén Fernández-Casal & Sonia Zaragoza & Paula Raña & Javier Tarrío-Saavedra, 2020. "Constructing a Control Chart Using Functional Data," Mathematics, MDPI, vol. 8(1), pages 1-26, January.
    18. Ana Justel & Marcela Svarc, 2018. "A divisive clustering method for functional data with special consideration of outliers," 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. 12(3), pages 637-656, September.
    19. Cristian F. Jiménez‐Varón & Fouzi Harrou & Ying Sun, 2024. "Pointwise data depth for univariate and multivariate functional outlier detection," Environmetrics, John Wiley & Sons, Ltd., vol. 35(5), August.
    20. Sara López-Pintado & Ying Sun & Juan Lin & Marc Genton, 2014. "Simplicial band depth for multivariate 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 321-338, September.

    More about this item

    Keywords

    FDA;

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:cte:wsrepe:ws140101. 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: Ana Poveda (email available below). General contact details of provider: http://portal.uc3m.es/portal/page/portal/dpto_estadistica .

    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.