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ON THE NONCENTRAL DISTRIBUTION OF A RANDOM MATRIX USEFUL IN CLASSIFICATION THEORY
Author(s) -
Rogers G. S.,
Kabe D. G.
Publication year - 1983
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1983.tb01196.x
Subject(s) - mathematics , discriminant function analysis , cauchy distribution , discriminant , statistic , statistics , linear discriminant analysis , random matrix , combinatorics , artificial intelligence , computer science , physics , eigenvalues and eigenvectors , quantum mechanics
Summary To prove the optimality properties of the maximum likelihood (and also minimum distance) discriminant rule Rogers (1980, p. 98) embeds the maximum likelihood discriminant function in a Cauchy‐Schwartz inequality. This embedding procedure of Rogers (1980) may be used to derive a new distribution for Anderson's (1958) classification statistic.