Rates of Convergence for Empirical Processes of Stationary Mixing Sequences

摘要

Classical empirical process theory for Vapnik- Cervonenkis classes deals mainlywith sequences of independent variables. This paper extends the theory to stationary sequences of dependent variables. It establishes rates of convergence for Beta-mixing empirical process indexed by classes of functions. The method of proof depends on a coupling of the dependent sequence with sequences of independent blocks, to which the classical theory can be applied. A uniform O(n-s/(1+s)) rate of convergence over V-C classes is established for sequences whose mixing coefficients decay slightly faster than O(n-s). (AN).