Bounds on expectations of order statistics for dependent samples

Arnold and Groeneveld (1979) presented distribution free bounds for E(Xg:n) the expected value of the gth order statistic when sampling n possibly dependent observations from populations each with finite expectations [mu]i and finite variances [sigma]2i. Here, the problem of incorporating known dependencies among the distributions of observations in a sample to produce bounds for the order statistics of that sample is considered. Limits are obtained for expectations of the gth order statistic and the range. These limits hold even when the population variances are not finite. An application of the upper bound for E(Xn:n) is given.