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Probability densities from distances and discrimination. (English) Zbl 0899.62076

Summary: Given a population and a random vector \(X\), by using distances between observations of \(X\), we prove that it is, in general, possible to construct probability densities for \(X\). This distance-based approach can present problems, from a multidimensional scaling point of view, for some monotonic density functions, where the construction must be made on the basis of symmetric functions instead of distances. A measure of divergence between the true density and this construction is given. The procedure aims to offer alternative methods for performing discriminant analysis.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
91C15 One- and multidimensional scaling in the social and behavioral sciences
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