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Title: Nonlinear principal and canonical directions from continuous extensions of multidimensional scaling
Author: Cuadras, C. M. (Carlos María)
Keywords: Estadística matemàtica
Polinomis ortogonals
Variables (Matemàtica)
Mathematical statistics
Orthogonal polynomials
Variables (Mathematics)
Issue Date: Feb-2014
Publisher: Scientific Research Publishing
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.
Note: Reproducció del document publicat a:
It is part of: Open Journal of Statistics, 2014, vol. 4, num. 2, p. 132-149
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ISSN: 2161-718X
Appears in Collections:Articles publicats en revistes (Genètica, Microbiologia i Estadística)

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