Expected Sample Moments of Concomitants of Selected Order Statistics

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. 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.