INTERPRETATION AND MANIPULATION OF EDGEWORTH EXPANSIONS

W. C. M. KALLENBERG

Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands

(Received May 27, 1991; revised May 11, 1992)

Abstract. With a given Edgeworth expansion sequences of i.i.d. r.v.’s are associated such that the Edgeworth expansion for the standardized sum of these r.v.’s agrees with the given Edgeworth expansion. This facilitates interpretation and manipulation of Edgeworth expansions. The theory is applied to the power of linear rank statistics and to the combination of such statistics based on subsamples. Complicated expressions for the power become more transparent. As a consequence of the sum-structure it is seen why splitting the sample causes no loss of first order efficiency and only a small loss of second order efficiency.

Key words and phrases: Asymptotic expansions, combination of test statistics, one-sample problem, two-sample problem, power, contiguous alternatives, second order efficiency, second order standardization.