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The Structure of Ellipsoidal Distributions I. Canonical Analysis
Author(s) -
Jensen D. R.
Publication year - 1984
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710260717
Subject(s) - ellipsoid , mathematics , principal component analysis , canonical correlation , canonical form , principal axis theorem , sample (material) , statistical physics , distribution (mathematics) , principal (computer security) , statistics , mathematical analysis , geometry , pure mathematics , computer science , physics , astronomy , thermodynamics , operating system
This study is concerned with the structure of variables having ellipsoidal distributions. In Part I it is shown that many normal‐theory results in canonical analysis are exact for all ellipsoidal distributions under a specified model for sampling. In Part II similar conclusions are drawn regarding the use of principal components. These findings suggest using normal‐theory procedures in canonical and principal components analyses as approximate large‐sample procedures for distributions attracted to ellipsoidal stable laws.