Second order and \(L^ p\)-comparisons between the boostrap and empirical Edgeworth expansion methodologies (Q1118922)

The boostrap estimate of distribution functions of studentized statistics is shown to be more accurate than even the two-term empirical Edgeworth expansion, thus strengthening the claim of superiority of the boostrap over the normal approximation method. The two methods are compared not only with respect to bounded bowl-shaped loss functions but also with respect to squared error loss and, more generally, in \(L^ p\)-norms.