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hal.structure.identifierCommonwealth Scientific and Industrial Research Organisation [Canberra] [CSIRO]
dc.contributor.authorBISHOP, Adrian N.
hal.structure.identifierQuality control and dynamic reliability [CQFD]
dc.contributor.authorDEL MORAL, Pierre
hal.structure.identifierÉcole normale supérieure de Lyon [ENS de Lyon]
dc.contributor.authorNICLAS, Angèle
dc.date.accessioned2024-04-04T03:07:38Z
dc.date.available2024-04-04T03:07:38Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193461
dc.description.abstractEnThis article provides a comprehensive, rigorous, and self-contained introduction to the analysis of Wishart matrix moments. This article may act as an introduction to some aspects of random matrix theory, or as a self-contained exposition of Wishart matrix moments. Random matrix theory plays a central role in nuclear and statistical physics, computational mathematics and engineering sciences, including data assimilation, signal processing, combinatorial optimization, compressed sensing, econometrics and mathematical finance, among numerous others. The mathematical foundations of the theory of random matrices lies at the intersection of combinatorics, non-commutative algebra, geometry, multivariate functional and spectral analysis, and of course statistics and probability theory. As a result, most of the classical topics in random matrix theory are technical, and mathematically difficult to penetrate for non-experts and regular users and practitioners. The technical aim of this article is to review and extend some important results in random matrix theory in the specific context of real random Wishart matrices. This special class of Gaussian-type sample covariance matrix plays an important role in multivariate analysis and in statistical theory. We derive non-asymptotic formulae for the full matrix moments of real valued Wishart random matrices. As a corollary, we derive and extend a number of spectral and trace-type results for the case of non-isotropic Wishart random matrices. We also derive the full matrix moment analogues of some classic spectral and trace-type moment results. For example, we derive semi-circle and Marchencko-Pastur-type laws in the non-isotropic and full matrix cases. Laplace matrix transforms and matrix moment estimates are also studied, along with new spectral and trace concentration-type inequalities.
dc.language.isoen
dc.title.enAn introduction to Wishart matrix moments
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Probabilités [math.PR]
dc.subject.halMathématiques [math]/Combinatoire [math.CO]
dc.identifier.arxiv1710.10864
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-01662575
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01662575v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=BISHOP,%20Adrian%20N.&DEL%20MORAL,%20Pierre&NICLAS,%20Ang%C3%A8le&rft.genre=preprint


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