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High dimensional statistical inference and random matrices. (English) Zbl 1120.62033
Sanz-Solé, Marta (ed.) et al., Proceedings of the international congress of mathematicians (ICM), Madrid, Spain, August 22–30, 2006. Volume I: Plenary lectures and ceremonies. Zürich: European Mathematical Society (EMS) (ISBN 978-3-03719-022-7/hbk). 307-333 (2007).
Summary: Multivariate statistical analysis is concerned with observations on several variables which are thought to possess some degree of inter-dependence. Driven by problems in genetics and the social sciences, it first flowered in the earlier half of the last century. Subsequently, random matrix theory (RMT) developed, initially within physics, and more recently widely in mathematics. While some of the central objects of study in RMT are identical to those of multivariate statistics, statistical theory was slow to exploit the connection. However, with vast data collections ever more common, data sets now often have as many or more variables than the number of individuals observed. In such contexts, the techniques and results of RMT have much to offer multivariate statistics. The paper reviews some of the progress to date.
For the entire collection see [Zbl 1111.00009].

MSC:
62Hxx Multivariate analysis
62H10 Multivariate distribution of statistics
15B52 Random matrices (algebraic aspects)
62H25 Factor analysis and principal components; correspondence analysis
62H20 Measures of association (correlation, canonical correlation, etc.)
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