p-Norm bounds on the expectation of the maximum of a possibly dependent sample

Let X1, X2,..., Xn be identically distributed possibly dependent random variables with finite pth absolute moment assumed without loss of generality to be equal to 1. Denote the order statistics by X1:n, X2:n,..., Xn:n. Bounds are derived for E(Xn:n) when it is assumed that the Xi's are (i) arbitrarily dependent and (ii) independent. The effect of assuming a symmetric common distribution for the Xi's is discussed. Analogous bounds are described for the expected range of the sample. Bounds on expectations of general linear combinations of order statistics are described in the independent case.