We consider a class of matrices of the form , where Xn is an nxN matrix consisting of i.i.d. standardized complex entries, is a nonnegative definite square root of the nonnegative definite Hermitian matrix An, and Bn is diagonal with nonnegative diagonal entries. Under the assumption that the...

A multi-resolution basis can provide a useful representation of nonstationary two-dimensional spatial processes that are typically encountered in the geosciences. The main advantages are its flexibility for representing departures from stationarity and importantly the scalability of algorithms...

We are concerned with the behavior of the eigenvalues of renormalized sample covariance matrices of the form Cn=np(1nAp1/2XnBnXn∗Ap1/2−1ntr(Bn)Ap) as p,n→∞ and p/n→0, where Xn is a p×n matrix with i.i.d. real or complex valued entries Xij satisfying E(Xij)=0, E|Xij|2=1 and having...

In some multivariate problems with missing data, pairs of variables exist that are never observed together. For example, some modern biological tools can produce data of this form. As a result of this structure, the covariance matrix is only partially identifiable, and point estimation requires...