The Law of the Iterated Logarithm for U-Processes

Sufficient conditions for the law of the iterated logarithm for non-degenerate U-processes are presented. The law of the iterated logarithm for V-C subgraph classes of functions is obtained under second moment of the envelope. A bracketing condition for the law of the iterated logarithm for U-processes is presented. Applications to the law of the iterated logarithm of U-statistics with estimated parameters and M-estimators are mentioned.