Berry-Esseen bounds for functionals of independent random variables

We derive Berry-Esseen approximation bounds for general functionals of independent random variables, based on a continuous-time integration by parts setting and discrete chaos expansions methods. Our approach improves related results obtained in discrete-time settings applies to U-statistics satisfying the weak assumption decomposability Hoeffding sense, yield Kolmogorov distance instead Wasserstein previously derived special case degenerate U-statistics. Linear quadratic arbitrary sequences variables are included as particular cases, with new fourth moment bounds, applications given decompositions, weighted U-statistics, forms, subgraph weighing. In our recover improve available literature, apply matrices non-empty diagonals.