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A Continuous Metric Scaling Solution for a Random Variable

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  • Cuadras, C. M.
  • Fortiana, J.

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.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:52:y:1995:i:1:p:1-14
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    Cited by:

    1. Alonso, Pablo J., 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.
    2. Michael Funke & Marc Gronwald, 2009. "A Convex Hull Approach to Counterfactual Analysis of Trade Openness and Growth," CESifo Working Paper Series 2692, CESifo.
    3. Cuadras, C. M., 2002. "On the Covariance between Functions," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 19-27, April.
    4. 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.
    5. Salinelli, Ernesto, 2009. "Nonlinear principal components, II: Characterization of normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 652-660, April.
    6. 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.
    7. 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.
    8. 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.
    9. Cuadras, Carles M. & Cuadras, Daniel, 2008. "Eigenanalysis on a bivariate covariance kernel," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2497-2507, November.
    10. 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.
    11. Aurea Grané & Rosario Romera, 2018. "On Visualizing Mixed-Type Data," Sociological Methods & Research, , vol. 47(2), pages 207-239, March.
    12. 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.

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