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Roy's largest root under rank-one alternatives:The complex valued case and applications
Prathapasinghe Dharmawansa, Boaz Nadler, Ofer Shwartz
The largest eigenvalue of a Wishart matrix, known as Roy's largest root (RLR), plays an important role in a variety of applications. Most works to date derived approximations to it…
Local Asymptotic Normality of the spectrum of high-dimensional spiked F-ratios
Prathapasinghe Dharmawansa, Iain M. Johnstone, Alexei Onatski
We consider two types of spiked multivariate F distributions: a scaled distribution with the scale matrix equal to a rank-one perturbation of the identity, and a distribution with…
Joint density of eigenvalues in spiked multivariate models
Prathapasinghe Dharmawansa, Iain M. Johnstone
The classical methods of multivariate analysis are based on the eigenvalues of one or two sample covariance matrices. In many applications of these methods, for example to high dim…
Three Problems Related to the Eigenvalues of Complex Non-central Wishart Matrices with a Rank-1 Mean
Prathapasinghe Dharmawansa
Recently, D. Wang has devised a new contour integral based method to simplify certain matrix integrals. Capitalizing on that approach, we derive a new expression for the probabilit…