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A Continuous Metric Scaling Solution for a Random Variable

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  • Cuadras, C. M.
  • Fortiana, J.
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    Abstract

    As a generalization of the classical metric scaling solution for a finite set of points, a countable set of uncorrelated random variables is obtained from an arbitary continuous random variable X. The properties of these variables allow us to regard them as principal axes for X with respect to the distance function d(u, v) = [formula]. Explicit results are obtained for uniform and negative exponential random variables.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 52 (1995)
    Issue (Month): 1 (January)
    Pages: 1-14

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    Handle: RePEc:eee:jmvana:v:52:y:1995:i:1:p:1-14

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    Cited by:
    1. 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, vol. 4(2), pages 207-261, December.
    2. Aurea Grane & Josep Fortiana, 2006. "Karhunen-Loève Basis In Goodness-Of-Fit Tests Decomposition: An Evaluation," Statistics and Econometrics Working Papers ws062710, Universidad Carlos III, Departamento de Estadística y Econometría.
    3. 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, vol. 9(1), pages 1-96, June.
    4. Cuadras, C. M., 2002. "On the Covariance between Functions," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 19-27, April.
    5. 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.
    6. Salinelli, Ernesto, 2009. "Nonlinear principal components, II: Characterization of normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 652-660, April.
    7. 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.
    8. Michael Funke & Marc Gronwald, 2009. "A Convex Hull Approach to Counterfactual Analysis of Trade Openness and Growth," CESifo Working Paper Series 2692, CESifo Group Munich.
    9. Irene Albarrán & Pablo Alonso & Aurea Grané, 2011. "Profile identification via weighted related metric scaling : an application to dependent Spanish children," Statistics and Econometrics Working Papers ws113628, Universidad Carlos III, Departamento de Estadística y Econometría.
    10. Cuadras, Carles M. & Cuadras, Daniel, 2008. "Eigenanalysis on a bivariate covariance kernel," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2497-2507, November.

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