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 arbitrary 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) = p ju \Gamma vj. Explicit results are obtained for uniform and negative exponential random variables. Keywords and Phrases Principal components of a stochastic process, Principal Coordinate Analysis. AMS Subject classification: 62H25 1 Introduction Metric Scaling or Principal Coordinate Analysis, introduced by Torgerson [14] and especially Gower [9], is a method of ordination aiming to provide a graphical representation of a finite set of n elements. The method obtains a n \Theta m matrix X from an n \Theta n Euclidean distance matrix \Delta = (ffi ij ) . The set of n rows of X, considered as points in R m , has interdistances which reproduce those in \Delta ...

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