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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Multivariate Statistical Analysis and Random Matrix Theory
verfasst von : Gregory S. Chirikjian
Erschienen in: Stochastic Models, Information Theory, and Lie Groups, Volume 2
Verlag: Birkhäuser Boston
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This chapter is concerned with a number of issues in statistics that have a grouptheoretic flavor. Large books can be found that are dedicated to each of the topics that are discussed briefly in the sections that follow. Although the coverage here is meant to be broad and introductory for the most part, effort is taken to elucidate connections between statistics and the theory of Lie groups, perhaps at the expense of completeness. The main topics covered are numerical sampling techniques, multivariate statistical analysis, and theory/numerical procedures associated with random orthogonal, positive definite, unitary, and Hermitian matrices. Integration on Lie groups and their homogeneous spaces ties these topics together. Pointers to classical applications in particle physics as well as more recent applications in complicated wireless communication networks are provided.