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...

We introduce a path following algorithm for "L"₁-regularized generalized linear models. The "L"₁-regularization procedure is useful especially because it, in effect, selects variables according to the amount of penalization on the "L"₁-norm of the coefficients, in a manner that is less greedy...

We propose the elastic net, a new regularization and variable selection method. Real world data and a simulation study show that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation. In addition, the elastic net encourages a grouping effect, where...