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High Dimensional Statistical Inference and Random Matrices

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arxiv math/0611589 v1 pith:AHB72FTH submitted 2006-11-19 math.ST math.PRstat.TH

Iain M. Johnstone This is my paper · ORCID
classification math.STmath.PRstat.TH
keywords multivariatesomestatisticaldatarandomstatisticstheoryvariables
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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 collection 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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A convergence framework for Airy$_\beta$ line ensemble via pole evolution

    math.PR 2024-11 accept novelty 8.0 of 10

    A pole-evolution characterization of the Airy_beta line ensemble yields convergence of DBM with general potentials, Laguerre, and Jacobi processes to the universal edge limit.

  2. A note on "The volume of random simplices from elliptical distributions in high dimension"

    math.ST 2026-07 unverdicted novelty 5.0 of 10

    The authors relax the closeness-to-identity condition in Assumption (B) of Gusakova et al. so that central and stable limit theorems for simplex volumes hold under spiked and Toeplitz covariance structures.

  3. Application of Random Matrix Theory in High-Dimensional Statistics

    stat.ME 2024-12 conditional novelty 3.0 of 10

    A review of RMT in high-dimensional statistics that contributes a new CLT for the log-eigenvalues of Wishart matrices, with a flawed proof.

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