Nonlinear principal and canonical directions from continuous extensions of multidimensional scaling
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...
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2014 |
| País: | España |
| Recursos: | Universidad de Barcelona |
| Repositório: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/65330 |
| Acesso em linha: | https://hdl.handle.net/2445/65330 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Estadística matemàtica Polinomis ortogonals Variables (Matemàtica) Mathematical statistics Orthogonal polynomials Variables (Mathematics) |
| Resumo: | 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. |
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