IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v117y2013icp14-31.html
   My bibliography  Save this article

Strong consistency of k-parameters clustering

Author

Listed:
  • Gallegos, María Teresa
  • Ritter, Gunter

Abstract

Pollard showed for k-means clustering and a very broad class of sampling distributions that the optimal cluster means converge to the solution of the related population criterion as the size of the data set increases. We extend this consistency result to k-parameters clustering, a method derived from the heteroscedastic, elliptical classification model. It allows a more sensitive data analysis and has the advantage of being affine equivariant. Moreover, the present theory yields a consistent criterion for selecting the number of clusters in such models.

Suggested Citation

  • Gallegos, María Teresa & Ritter, Gunter, 2013. "Strong consistency of k-parameters clustering," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 14-31.
    • Handle: RePEc:eee:jmvana:v:117:y:2013:i:c:p:14-31
    DOI: 10.1016/j.jmva.2013.01.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X13000146
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2013.01.013?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. Kiefer, Nicholas M, 1978. "Discrete Parameter Variation: Efficient Estimation of a Switching Regression Model," Econometrica, Econometric Society, vol. 46(2), pages 427-434, March.
    2. Robert Tibshirani & Guenther Walther & Trevor Hastie, 2001. "Estimating the number of clusters in a data set via the gap statistic," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 411-423.
    3. María Gallegos & Gunter Ritter, 2009. "Trimming algorithms for clustering contaminated grouped data and their robustness," 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. 3(2), pages 135-167, September.
    4. Gallegos, María Teresa & Ritter, Gunter, 2010. "Using combinatorial optimization in model-based trimmed clustering with cardinality constraints," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 637-654, March.
    5. Bertrand, P. & Bel Mufti, G., 2006. "Loevinger's measures of rule quality for assessing cluster stability," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 992-1015, February.
    6. Hans Bock, 1972. "Statistische Modelle und Bayessche Verfahren zur Bestimmung einer unbekannten Klassifikation normalverteilter zufälliger Vektoren," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 18(1), pages 120-132, December.
    7. Hennig, Christian, 2007. "Cluster-wise assessment of cluster stability," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 258-271, September.
    8. Peter Bryant, 1991. "Large-sample results for optimization-based clustering methods," Journal of Classification, Springer;The Classification Society, vol. 8(1), pages 31-44, January.
    9. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    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. María Teresa Gallegos & Gunter Ritter, 2018. "Probabilistic clustering via Pareto solutions and significance tests," 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(2), pages 179-202, June.
    2. Chakraborty, Saptarshi & Das, Swagatam, 2021. "On uniform concentration bounds for Bi-clustering by using the Vapnik–Chervonenkis theory," Statistics & Probability Letters, Elsevier, vol. 175(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. María Teresa Gallegos & Gunter Ritter, 2018. "Probabilistic clustering via Pareto solutions and significance tests," 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(2), pages 179-202, June.
    2. Fritz, Heinrich & García-Escudero, Luis A. & Mayo-Iscar, Agustín, 2013. "A fast algorithm for robust constrained clustering," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 124-136.
    3. Maldonado, Wilfredo L. & Tourinho, Octávio A.F. & Valli, Marcos, 2012. "Exchange rate bubbles: Fundamental value estimation and rational expectations test," Journal of International Money and Finance, Elsevier, vol. 31(5), pages 1033-1059.
    4. Šárka Brodinová & Peter Filzmoser & Thomas Ortner & Christian Breiteneder & Maia Rohm, 2019. "Robust and sparse k-means clustering 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. 13(4), pages 905-932, December.
    5. Fritz, Heinrich & García-Escudero, Luis A. & Mayo-Iscar, Agustín, 2012. "tclust: An R Package for a Trimming Approach to Cluster Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 47(i12).
    6. Hsu, David, 2015. "Comparison of integrated clustering methods for accurate and stable prediction of building energy consumption data," Applied Energy, Elsevier, vol. 160(C), pages 153-163.
    7. Jonas M. B. Haslbeck & Dirk U. Wulff, 2020. "Estimating the number of clusters via a corrected clustering instability," Computational Statistics, Springer, vol. 35(4), pages 1879-1894, December.
    8. Gallegos, María Teresa & Ritter, Gunter, 2010. "Using combinatorial optimization in model-based trimmed clustering with cardinality constraints," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 637-654, March.
    9. P.A.V.B. Swamy & I-Lok Chang & Jatinder S. Mehta & William H. Greene & Stephen G. Hall & George S. Tavlas, 2016. "Removing Specification Errors from the Usual Formulation of Binary Choice Models," Econometrics, MDPI, vol. 4(2), pages 1-21, June.
    10. Carlo Altavilla & Raffaella Giacomini & Giuseppe Ragusa, 2017. "Anchoring the yield curve using survey expectations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(6), pages 1055-1068, September.
    11. Fernando Rios-Avila & Gustavo Canavire-Bacarreza, 2018. "Standard-error correction in two-stage optimization models: A quasi–maximum likelihood estimation approach," Stata Journal, StataCorp LP, vol. 18(1), pages 206-222, March.
    12. Sandy Fréret & Denis Maguain, 2017. "The effects of agglomeration on tax competition: evidence from a two-regime spatial panel model on French data," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 24(6), pages 1100-1140, December.
    13. Ai, Chunrong & Chen, Xiaohong, 2007. "Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables," Journal of Econometrics, Elsevier, vol. 141(1), pages 5-43, November.
    14. Thiemo Fetzer & Samuel Marden, 2017. "Take What You Can: Property Rights, Contestability and Conflict," Economic Journal, Royal Economic Society, vol. 0(601), pages 757-783, May.
    15. Gregory, Allan W. & McCurdy, Thomas H., 1986. "The unbiasedness hypothesis in the forward foreign exchange market: A specification analysis with application to France, Italy, Japan, the United Kingdom and West Germany," European Economic Review, Elsevier, vol. 30(2), pages 365-381, April.
    16. Georgiev, Iliyan, 2010. "Model-based asymptotic inference on the effect of infrequent large shocks on cointegrated variables," Journal of Econometrics, Elsevier, vol. 158(1), pages 37-50, September.
    17. Daniel Agness & Travis Baseler & Sylvain Chassang & Pascaline Dupas & Erik Snowberg, 2022. "Valuing the Time of the Self-Employed," CESifo Working Paper Series 9567, CESifo.
    18. B. Praag & T. Dijkstra & J. Velzen, 1985. "Least-squares theory based on general distributional assumptions with an application to the incomplete observations problem," Psychometrika, Springer;The Psychometric Society, vol. 50(1), pages 25-36, March.
    19. Reischmann, Markus, 2016. "Creative accounting and electoral motives: Evidence from OECD countries," Journal of Comparative Economics, Elsevier, vol. 44(2), pages 243-257.
    20. Czudaj Robert L., 2020. "The role of uncertainty on agricultural futures markets momentum trading and volatility," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 24(3), pages 1-39, 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:eee:jmvana:v:117:y:2013:i:c:p:14-31. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.