Before revision:  Our main results are non-asymptotic and imply asymptotic uniform validity over large classes of models\to  .
After revision:  Our main results are non-asymptotic and imply asymptotic uniform validity over large classes of models\to 0; L is the operator norm of the functional, measuring the degree of its non-regularity, with L diverging for local functionals (or under weak identification of the global functionals) .