Empirical correlation operator and many-dimensional Hermite polynomials
This paper deals with an operator, which the author calls an empirical correlation operator, operating on the subspace of vector Hermite polynomials of a given order. The asymptotic properties of this operator are studied by considering a simple random sample of size \(n\) from an \(m\)-variate Gaussian population. The results obtained in this paper extend earlier results on the asymptotic behaviour of the spectrum of the operator when \(n\) and \(m\) go to infinity with \(m/n\) going to a finite quantity.
scientific article; zbMATH DE number 652264
scientific article