  We derive Stein approximation bounds for functionals of uniform random
variables, using chaos expansions and the Clark-Ocone representation formula
combined with derivation and finite difference operators. This approach covers
sums and functionals of both continuous and discrete independent random
variables. For random variables admitting a continuous density, it recovers
classical distance bounds based on absolute third moments, with better and
explicit constants. We also apply this method to multiple stochastic integrals
that can be used to represent U-statistics, and include linear and quadratic
functionals as particular cases.
