Asymptotic, Higher Order

Abstract

Higher order asymptotic deals with two sorts of closely related things. First, there are questions of approximation. One is concerned with expan- sions or inequalities for a distribution function. Second, there are inferential issues. These involve, among other things, the application of the ideas of the study of higher order e¢ ciency, admissibility and minimaxity. In the matter of expansions, it is as important to have usable, explicit formulas as a rigor- ous proof that the expansions are valid in the sense of truly approximating a target quantity up to the claimed degree of accuracy