A Robustness Property of the Projection Pursuit Methods in Sampling from Separably Dependent Random Vectors

Abstract

A purpose of thîs paper Is to point out that the dependence of the observations may Improve the capability of a P.P.M. (Projection Pursuit Method) In detecting clusters In the projected observation values. To this purpose, the mean vector and the covarlance matrix of the r.v. (random variables) representing the projected observation values are calculated under the assumptions of the Intrinsic Inference Model for Finite Populations of Separably Dependent Random Vectors. Comparison with the mean vector and the covarlance matrix under the assumption of 2 population of Independent r.vt. (random vectors) shows the effect of the dependence. It Is proved, at least for the case of normal r.v., that the probability that the projected observation values are sepa-reted Into two destinct clusters Is greater In the case of dependent r.vt. than In the case of Independent r.vt..