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Estimation of Principal Points
Author(s) -
Flury Bernard D.
Publication year - 1993
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.2307/2347416
Subject(s) - statistics , principal (computer security) , estimation , mathematics , computer science , engineering , systems engineering , operating system
SUMMARY The k principal points of a p ‐variate random vector X are defined as those points ξ 1 , . . ., ξ k which minimize the expected squared distance between X and the nearest of the ξ j . 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.