A comparison theorem on moment inequalities between negatively associated and independent random variables

Let {X-i, 1 less than or equal to i less than or equal to n} be a negativel y associated sequence, and let {X-i*, 1 less than or equal to i less than o r equal to n} be a sequence of independent random variables such that X-i* and X-i have the same distribution for each i = 1,2,...,n. It is shown in t his paper that Ef(Sigma(i=1)(n) X-i) less than or equal to Ef(Sigma(i=1)(n) X-i(*)) for any convex function f on R-1 and that Ef(max(1 less than or eq ual to k less than or equal to n) Sigma(i=k)(n) X-i) less than or equal to Ef(max(1 less than or equal to k less than or equal to n) Sigma(i=1)X(i)*) for any increasing convex function. Hence, most of the well-known inequalit ies, such as the Rosenthal maximal inequality and the Kolmogorov exponentia l inequality, remain true For negatively associated random variables. In pa rticular, the comparison theorem on moment inequalities between negatively associated iind independent random variables extends the Hoeffding inequali ty on the probability bounds for the sum of a random sample without replace ment from a finite population.