IDEAS home Printed from https://ideas.repec.org/p/cte/wsrepe/ws098526.html
   My bibliography  Save this paper

Recombining dependent data: an Order Statistics

Author

Listed:
  • Álvarez, Adolfo
  • Peña, Daniel

Abstract

This article discusses the problem of forming groups from previously split data. Algorithms for Cluster Analysis like SAR proposed by Peña, Rodriguez and Tiao (2004), divide the sample into small very homogeneous groups and then recombine them to form the definitive data configuration. This kind of splitting leads to dependent data in the sense that the groups are disjoint, so no traditional homogeneity of means or variances tests can be used. We propose an alternative by using Order Statistics. Studying the distribution and some moments of linear combination of Order Statistics it is possible to recombine disjoint data groups when they merge into a sample from the same population.

Suggested Citation

  • Álvarez, Adolfo & Peña, Daniel, 2009. "Recombining dependent data: an Order Statistics," DES - Working Papers. Statistics and Econometrics. WS ws098526, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws098526
    as

    Download full text from publisher

    File URL: https://e-archivo.uc3m.es/rest/api/core/bitstreams/c5543b3b-ebef-4e0b-b8fc-4e5bb8b4ae24/content
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. A. D. Hutson & M. D. Ernst, 2000. "The exact bootstrap mean and variance of an L‐estimator," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 89-94.
    2. R. Gnanadesikan & J. Kettenring & S. Tsao, 1995. "Weighting and selection of variables for cluster analysis," Journal of Classification, Springer;The Classification Society, vol. 12(1), pages 113-136, March.
    3. Pena D. & Prieto F.J., 2001. "Cluster Identification Using Projections," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1433-1445, December.
    4. Raftery, Adrian E. & Dean, Nema, 2006. "Variable Selection for Model-Based Clustering," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 168-178, March.
    5. A. Azzalini & A.W. Bowman, 1990. "A Look at Some Data on the Old Faithful Geyser," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 39(3), pages 357-365, November.
    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. Douglas Steinley & Michael Brusco, 2008. "Selection of Variables in Cluster Analysis: An Empirical Comparison of Eight Procedures," Psychometrika, Springer;The Psychometric Society, vol. 73(1), pages 125-144, March.
    2. Tsai, Chieh-Yuan & Chiu, Chuang-Cheng, 2008. "Developing a feature weight self-adjustment mechanism for a K-means clustering algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4658-4672, June.
    3. Susan Brudvig & Michael J. Brusco & J. Dennis Cradit, 2019. "Joint selection of variables and clusters: recovering the underlying structure of marketing data," Journal of Marketing Analytics, Palgrave Macmillan, vol. 7(1), pages 1-12, March.
    4. Lauer, Alexandra & Zähle, Henryk, 2017. "Bootstrap consistency and bias correction in the nonparametric estimation of risk measures of collective risks," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 99-108.
    5. Giuseppe RICCIARDO LAMONICA, 2002. "La funzionalita' nelle zone omogenee delle Marche," Working Papers 165, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    6. Hirukawa, Masayuki, 2010. "Nonparametric multiplicative bias correction for kernel-type density estimation on the unit interval," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 473-495, February.
    7. Mark S. Handcock & Adrian E. Raftery & Jeremy M. Tantrum, 2007. "Model‐based clustering for social networks," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(2), pages 301-354, March.
    8. Jerzy Korzeniewski, 2016. "New Method Of Variable Selection For Binary Data Cluster Analysis," Statistics in Transition New Series, Polish Statistical Association, vol. 17(2), pages 295-304, June.
    9. Ricardo Fraiman & Badih Ghattas & Marcela Svarc, 2013. "Interpretable clustering using unsupervised binary trees," 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. 7(2), pages 125-145, June.
    10. Jian Guo & Elizaveta Levina & George Michailidis & Ji Zhu, 2010. "Pairwise Variable Selection for High-Dimensional Model-Based Clustering," Biometrics, The International Biometric Society, vol. 66(3), pages 793-804, September.
    11. Loperfido, Nicola, 2021. "Some theoretical properties of two kurtosis matrices, with application to invariant coordinate selection," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    12. Maugis, C. & Celeux, G. & Martin-Magniette, M.-L., 2011. "Variable selection in model-based discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1374-1387, November.
    13. Ahlquist, John S. & Breunig, Christian, 2009. "Country clustering in comparative political economy," MPIfG Discussion Paper 09/5, Max Planck Institute for the Study of Societies.
    14. Cathy Maugis & Gilles Celeux & Marie-Laure Martin-Magniette, 2009. "Variable Selection for Clustering with Gaussian Mixture Models," Biometrics, The International Biometric Society, vol. 65(3), pages 701-709, September.
    15. Renato Cordeiro Amorim, 2016. "A Survey on Feature Weighting Based K-Means Algorithms," Journal of Classification, Springer;The Classification Society, vol. 33(2), pages 210-242, July.
    16. Fred Huffer & Cheolyong Park, 2000. "A test for multivariate structure," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(5), pages 633-650.
    17. Jeffrey Andrews & Paul McNicholas, 2014. "Variable Selection for Clustering and Classification," Journal of Classification, Springer;The Classification Society, vol. 31(2), pages 136-153, July.
    18. Alessandro Casa & Andrea Cappozzo & Michael Fop, 2022. "Group-Wise Shrinkage Estimation in Penalized Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 648-674, November.
    19. Wang, Ketong & Porter, Michael D., 2018. "Optimal Bayesian clustering using non-negative matrix factorization," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 395-411.
    20. Csereklyei, Zsuzsanna & Anantharama, Nandini & Kallies, Anne, 2021. "Electricity market transitions in Australia: Evidence using model-based clustering," Energy Economics, Elsevier, vol. 103(C).

    More about this item

    Keywords

    SAR;

    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:ws098526. 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.