Multivariate Procedures Invariant Under Linear Transformations

Many well-known procedures in multivariate data analysis are invariant under the group, L(p), of translations and nonsingular linear transformations. New maximal L(p) invariant statistics are derived and are shown to have the geometrical interpretation of a scatter of points in Euclidean space. The...

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Bibliographic Details
Published in:The Annals of mathematical statistics 1971-10, Vol.42 (5), p.1569-1578
Main Author: Obenchain, R. L.
Format: Article
Language:English
Subjects:
Coordinate systems
Euclidean space
Linear transformations
Mathematical procedures
Mathematical vectors
Matrices
Null hypothesis
Population distributions
Statistics
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Summary:Many well-known procedures in multivariate data analysis are invariant under the group, L(p), of translations and nonsingular linear transformations. New maximal L(p) invariant statistics are derived and are shown to have the geometrical interpretation of a scatter of points in Euclidean space. The distribution of maximal L(p) invariants for the case of a single multivariate normal population is shown to follow from a result of James (1954). Finally we consider tests of the null hypothesis that$k > 1$populations are identical and show that optimal L(p) invariant tests are similar tests of randomness.
ISSN:0003-4851
2168-8990
DOI:10.1214/aoms/1177693155