Multivariate Statistical Analysis: A Geometric Perspective

2009/02/03 by Yuri N. Tyurin, Tyurin, Yuri N.
Mathematics · #62H12 (Primary) 62J05 #62H15 #62J12 (Secondary) #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #msc:62H12 #msc:62H15 #msc:62J05 #msc:62J12 #stat.TH

paper · pdf · doi:10.48550/arxiv.0902.0408

25 pages

arxiv created 2009/02/03 · arxiv updated 2009/12/01

Abstract

A new, coordinate-free (geometric) approach to multivariate statistical analysis. General multivariate linear models and linear hypotheses are defined in geometric form. A method of constructing statistical criteria is defined for linear hypotheses. As a result, multivariate statistical analysis is developed in full analogy to classical statistical analysis. This approach is based on tensor products and modules over the ring of square matrices, supplied with an inner product.

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