Estimation of Principal Points

Bernard D. Flury

Journal of the Royal Statistical Society Series C, 1993, vol. 42, issue 1, 139-151

Abstract: The k principal points of a p‐variate random vector X are defined as those points ξ1, . . ., ξk which minimize the expected squared distance between X and the nearest of the ξj. This paper reviews some of the theory of principal points and redefines them in terms of self‐consistent points. An anthropometrical problem which initiated the theoretical developments is described. Four methods of estimation, ranging from normal theory maximum likelihood to the usual k‐means algorithm in cluster analysis, are introduced and applied to the example. Finally, a leave‐one‐out method is used to assess the performance of the four methods.

Date: 1993
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