Comparison theorems, random geometry and some limit theorems for empirical processes
A new comparison theorem for Rademacher averages is obtained and by this result the law of the iterated logarithm and the law of large numbers for empirical processes indexed by a family of square integrable functions are proved. The conditions for fulfilling of these laws are quite analogous to the classical conditions of Kolmogorov and Prokhorov. The characterization of the law of the iterated logarithm for empirical processes under some random geometric conditions is also obtained.
scientific article; zbMATH DE number 4113665