Abstract: We establish some asymptotic results for the statistic T(Fn) and the corresponding jackknife estimators, where Fn is the empirical distribution and T is a second-order differentiable functional in some sense. In particular, second-order asymptotic representations of T(Fn) and the jackknife estimator are obtained and the jackknife variance and bias estimators are shown to be consistent.
Key words and phrases: Asymptotic representation, bias, consistency, statistical functional, variance.