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Notes on asymptotics of sample eigenstructure for spiked covariance models with non-Gaussian data
Iain M. Johnstone, Jeha Yang
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 sa…
Asymptotics of eigenstructure of sample correlation matrices for high-dimensional spiked models
David Morales-Jimenez, Iain M. Johnstone, Matthew R. McKay +1
Sample correlation matrices are employed ubiquitously in statistics. However, quite surprisingly, little is known about their asymptotic spectral properties for high-dimensional da…
Spiked covariances and principal components analysis in high-dimensional random effects models
Zhou Fan, Iain M. Johnstone, Yi Sun
We study principal components analyses in multivariate random and mixed effects linear models, assuming a spherical-plus-spikes structure for the covariance matrix of each random e…
Edgeworth correction for the largest eigenvalue in a spiked PCA model
Jeha Yang, Iain M. Johnstone
We study improved approximations to the distribution of the largest eigenvalue of the sample covariance matrix of zero-mean Gaussian observations in dimension $p+1…
On Minimax Optimality of Sparse Bayes Predictive Density Estimates
Gourab Mukherjee, Iain M. Johnstone
We study predictive density estimation under Kullback-Leibler loss in -sparse Gaussian sequence models. We propose proper Bayes predictive density estimates and establish a…
Tail sums of Wishart and GUE eigenvalues beyond the bulk edge
Iain M. Johnstone
Consider the classical Gaussian unitary ensemble of size and the real Wishart ensemble . In the limits as and , the expected number of ei…