Abstract The Davis–Kahan theorem is used in the analysis of many statistical procedures to
bound the distance between subspaces spanned by population eigenvectors and their …

Let be an n by p data matrix, where the n rows form a random sample of size n from a certain
p-dimensional population distribution. Let be the p× p sample correlation coefficient matrix …

Let Bn=(1/N) T1/2 n Xn X* n T1/2 n where Xn is nx N with iid complex standardized entries
having finite fourth moment, and T1/2 n is a Hermitian square root of the nonnegative …

Eigenvectors and eigenvalues are numbers and vectors associated to square matrices, and
together they provide the eigen-decomposition of a matrix which analyzes the structure of …

A vast literature has been devoted to the assessment of the proper number of eigenvalues
that have to be retained in Principal Components Analysis. Most of the publications are …

In applying statistical methods such as principal component analysis, canonical correlation
analysis, and sufficient dimension reduction, we need to determine how many eigenvectors …

The notion of probability density for a random function is not as straight-forward as in finite-
dimensional cases. While a probability density function generally does not exist for …

In classical analysis of variance, dispersion is measured by considering squared distances
of sample elements from the sample mean. We consider a measure of dispersion for …

In statistics and machine learning, we are interested in the eigenvectors (or singular vectors)
of certain matrices (eg covariance matrices, data matrices, etc). However, those matrices are …

This paper shows that a quadratic form in a multivariate sample has a certain rank and its
nonzero eigenvalues are distinct with probability one under the assumption that the matrix …