Expected sample moments of concomitants of selected order statistics

Authors:
Dirk V. Arnold;Hans-Georg Beyer
Affiliations:
Faculty of Computer Science, Dalhousie University, Halifax, Canada B3H 1W5;Department of Computer Science, Vorarlberg University of Applied Sciences, Dornbirn, Austria A-6850
Venue:
Statistics and Computing
Year:
2005

Citing 4
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Abstract

In this paper, the task of determining expected values of sample moments, where the sample members have been selected based on noisy information, is considered. This task is a recurring problem in the theory of evolution strategies. Exact expressions for expected values of sums of products of concomitants of selected order statistics are derived. Then, using Edgeworth and Cornish-Fisher approximations, explicit results that depend on coefficients that can be determined numerically are obtained. While the results are exact only for normal populations, it is shown experimentally that including skewness and kurtosis in the calculations can yield greatly improved results for other distributions.