IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v33y1997i4p405-411.html
   My bibliography  Save this article

Probability densities from distances and discrimination

Author

Listed:
  • Cuadras, C. M.
  • Atkinson, R. A.
  • Fortiana, J.

Abstract

Given a population and a random vector X, by using distances between observations of X, we prove that it is, in general, possible to construct probability densities for X. This distance-based approach can present problems, from a multidimensional scaling point of view, for some monotonic density functions, where the construction must be made on the basis of symmetric functions instead of distances. A measure of divergence between the true density and this construction is given. The procedure aims to offer alternative methods for performing discriminant analysis.

Suggested Citation

  • Cuadras, C. M. & Atkinson, R. A. & Fortiana, J., 1997. "Probability densities from distances and discrimination," Statistics & Probability Letters, Elsevier, vol. 33(4), pages 405-411, May.
    • Handle: RePEc:eee:stapro:v:33:y:1997:i:4:p:405-411
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(96)00154-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Cuadras, C. M. & Fortiana, J., 1995. "A Continuous Metric Scaling Solution for a Random Variable," Journal of Multivariate Analysis, Elsevier, vol. 52(1), pages 1-14, January.
    2. Cuadras, C. M., 1992. "Probability distributions with given multivariate marginals and given dependence structure," Journal of Multivariate Analysis, Elsevier, vol. 42(1), pages 51-66, July.
    3. W. Krzanowski, 1994. "Ordination in the presence of group structure, for general multivariate data," Journal of Classification, Springer;The Classification Society, vol. 11(2), pages 195-207, September.
    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. Aurea Grané & Rosario Romera, 2018. "On Visualizing Mixed-Type Data," Sociological Methods & Research, , vol. 47(2), pages 207-239, March.
    2. Albarrán Lozano, Irene & Alonso, Pablo J. & Grané Chávez, Aurea, 2011. "Profile identification via weighted related metric scaling : an application to dependent Spanish children," DES - Working Papers. Statistics and Econometrics. WS ws113628, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Cuadras, C. M., 2002. "On the Covariance between Functions," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 19-27, April.
    4. Nabil Kazi-Tani & Didier Rullière, 2019. "On a construction of multivariate distributions given some multidimensional marginals," Post-Print hal-01575169, HAL.
    5. Michael Funke & Marc Gronwald, 2009. "A Convex Hull Approach to Counterfactual Analysis of Trade Openness and Growth," Quantitative Macroeconomics Working Papers 20906, Hamburg University, Department of Economics.
    6. Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
    7. Grané, Aurea & Fortiana, Josep, 2006. "Karhunen-loève basis in goodness-of-fit tests decomposition: an evaluation," DES - Working Papers. Statistics and Econometrics. WS ws062710, Universidad Carlos III de Madrid. Departamento de Estadística.
    8. Eustasio Barrio & Juan Cuesta-Albertos & Carlos Matrán & Sándor Csörgö & Carles Cuadras & Tertius Wet & Evarist Giné & Richard Lockhart & Axel Munk & Winfried Stute, 2000. "Contributions of empirical and quantile processes to the asymptotic theory of goodness-of-fit tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(1), pages 1-96, June.
    9. Sugata Ghosh & Subhajit Dutta & Marc G. Genton, 2017. "A note on inconsistent families of discrete multivariate distributions," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-13, December.
    10. John Gower & Niel Roux & Sugnet Gardner-Lubbe, 2014. "The Canonical Analysis of Distance," Journal of Classification, Springer;The Classification Society, vol. 31(1), pages 107-128, April.
    11. Marian Núñez & Angel Villarroya & José María Oller, 2003. "Minimum Distance Probability Discriminant Analysis for Mixed Variables," Biometrics, The International Biometric Society, vol. 59(2), pages 248-253, June.
    12. Kaiser, Mark S. & Cressie, Noel, 2000. "The Construction of Multivariate Distributions from Markov Random Fields," Journal of Multivariate Analysis, Elsevier, vol. 73(2), pages 199-220, May.
    13. Nabil Kazi-Tani & Didier Rullière, 2017. "On a construction of multivariate distributions given some multidimensional marginals," Working Papers hal-01575169, HAL.
    14. Itziar Irigoien & Concepcion Arenas & Elena Fernández & Francisco Mestres, 2010. "GEVA: geometric variability-based approaches for identifying patterns in data," Computational Statistics, Springer, vol. 25(2), pages 241-255, June.
    15. Salinelli, Ernesto, 2009. "Nonlinear principal components, II: Characterization of normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 652-660, April.
    16. Cuadras, Carles M. & Cuadras, Daniel, 2008. "Eigenanalysis on a bivariate covariance kernel," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2497-2507, November.
    17. Grané, Aurea & Salini, Silvia & Verdolini, Elena, 2021. "Robust multivariate analysis for mixed-type data: Novel algorithm and its practical application in socio-economic research," Socio-Economic Planning Sciences, Elsevier, vol. 73(C).
    18. Cuadras, Carles M., 2015. "Contributions to the diagonal expansion of a bivariate copula with continuous extensions," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 28-44.
    19. D. Cox & M. Bayarri & M. Bayarri & C. Cuadras & Jośe Bernadro & F. Girón & E. Moreno & N. Keiding & D. Lindley & L. Pericchi & L. Piccinato & N. Reid & N. Wermuth, 1995. "The relation between theory and application in statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 4(2), pages 207-261, December.

    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:stapro:v:33:y:1997:i:4:p:405-411. 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.