ERA's: A New Approach to Small Sample Theory
This article proposes a new approach to small sample theory that achieves a meaningful integration of earlier directions of research in this ﬁeld. The approach centers on the constructive technique of approximating distributions developed recently by the author in . This technique utilizes extended rational approximants (ERA’s) which methods (such as those based on asymptotic expansions) and which simultaneously blend information from diverse analytic, numerical and experimental sources. The ﬁrst part of the article explores the general theory of approximation of continuous probability distributions by means of ERA’s. Existence, characterization, error bound and uniqueness for the convergence result obtained earlier in . Some further aspects of ﬁnding ERA’s by modiﬁcations to multiple-point Padé approximants are presented and the new approach is applied to the non-circular serial correlation coeﬀicient. The results of this application demonstrate how ERA’s provide systematic improvements over Edgeworth and saddlepoint techniques. These results, taken with those of the earlier article , suggest that the approach oﬀers considerable potential for empirical application in terms of its reliability, convenience and generality.
Phillips, Peter C.B., "ERA's: A New Approach to Small Sample Theory" (1982). Cowles Foundation Discussion Papers. 880.