CONDITIONING AND CONCENTRATION OF PRINCIPAL COMPONENTS

summary This paper uses various gauges to construct principal variables that satisfy criteria of maximal scatter. The solutions coincide with Hotelling's (1933) principal components in structured ensembles and mixtures, including heavy-tailed distributions not having moments. Thus, normal-theory tests are exact in level and power under nonstandard models allowing for correlated vector observations and for certain mixtures having neither moments nor unimodal marginals.

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