Notes on asymptotics of sample eigenstructure for spiked covariance models with non-Gaussian data

Iain M. Johnstone; Jeha Yang

Notes on asymptotics of sample eigenstructure for spiked covariance models with non-Gaussian data

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arxiv 1810.10427 v2 pith:BPVGX2QV submitted 2018-10-24 math.ST stat.TH

Iain M. Johnstone , Jeha Yang This is my paper · ORCID

classification math.STstat.TH

keywords resultssamplecovariancegivenmodelmorales-jimeneznon-gaussiannotes

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These expository notes serve as a reference for an accompanying post Morales-Jimenez et al. [2018]. In the spiked covariance model, we develop results on asymptotic normality of sample leading eigenvalues and certain projections of the corresponding sample eigenvectors. The results parallel those of Paul [2007], but are given using the non-Gaussian model of Bai and Yao [2008]. The results are not new, and citations are given, but proofs are collected and organized as a point of departure for Morales-Jimenez et al. [2018].

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Estimation of the number of principal components in high-dimensional multivariate extremes
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AIC and BIC rules for the number of significant principal components in multivariate extremes are developed and shown to be weakly consistent under a spiked covariance model.

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