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 negatively associated sequence, and let {X-i*, 1 less than or equal to i less than or 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 this 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 equal 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 inequalities, such as the Rosenthal maximal inequality and the Kolmogorov exponential inequality, remain true For negatively associated random variables. In particular, the comparison theorem on moment inequalities between negatively associated iind independent random variables extends the Hoeffding inequality on the probability bounds for the sum of a random sample without replacement from a finite population.