CONVERGENCE RATE IN CLT FOR VECTOR-VALUED RANDOM FIELDS
Abstract: Statistical version of the central limit theorem (CLT) with random matrix
normalization is established for random fields with values in a space ().
Dependence structure of the field under consideration is described in terms of the covariance
inequalities for the class of bounded Lipschitz ”test functions” defined on finite disjoint
collections of random vectors constituting the field. The main result provides an estimate of
the convergence rate, over a family of convex bounded sets, in the CLT with random
2000 AMS Mathematics Subject Classification: 60F0S, 60F2S, 62E20, 62H20.
Key words and phrases: Random fields, dependence conditions, CLT, random matrix
normalization, convergence rate.