Empirical bounds for functions with weak interactions

We provide sharp empirical estimates of expectation, variance and normal approximation for a class of statistics whose variation in any argument does not change too much when another argument is modified. Examples of such weak interactions are furnished by \(U\)- and \(V\)-statistics, Lipschitz \(L\)- statistics and various error functionals of \(L_2\)-regularized algorithms and Gibbs algorithms.