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C. M. Cuadras, E. A. Atkinson and J. Fortiana, “Probability Densities from Distances and Discriminant Analysis,” Statistics and Probability Letters, Vol. 33, No. 4, 1997, pp. 405-411. http://dx.doi.org/10.1016/S0167-7152(96)00154-X

has been cited by the following article:

• TITLE: Nonlinear Principal and Canonical Directions from Continuous Extensions of Multidimensional Scaling

  AUTHORS: Carles M. Cuadras

  KEYWORDS: Statistical Distances; Orthogonal Expansions; Principal Directions of Random Variables; Diagonal Expansions; Copulas; Uncountable Dimensionality

  JOURNAL NAME: Open Journal of Statistics, Vol.4 No.2, February 27, 2014

  ABSTRACT: A continuous random variable is expanded as a sum of a sequence of uncorrelated random variables. These variables are principal dimensions in continuous scaling on a distance function, as an extension of classic scaling on a distance matrix. For a particular distance, these dimensions are principal components. Then some properties are studied and an inequality is obtained. Diagonal expansions are considered from the same continuous scaling point of view, by means of the chi-square distance. The geometric dimension of a bivariate distribution is defined and illustrated with copulas. It is shown that the dimension can have the power of continuum.