In applying statistical methods such as principal component analysis, canonical correlation analysis, and sufficient dimension reduction, we need to determine how many eigenvectors of a random matrix ...

We develop a novel approach to identify regions of the genome underlying population genetic differentiation in any genetic data where the underlying population structure is unknown, or where the ...

Refined estimates for finite element or, more generally, Galerkin approximations of the eigenvalues and eigenvectors of selfadjoint eigenvalue problems are presented. More specifically, refined ...