In this section we prove a theorem that allows us to show asymptotic normality for sums of random variables for certain statistical problems with a limited amount of dependence between the variables. A sequence of random variables, Y 1, Y 2,…, is said to be m-dependent if for every integer, s ≥ 1, the sets of random variables {Y 1, …, Y s } and {Y m + s + 1,Y m + s + 2,…} are independent. (For m = 0, this is equivalent to independence of the sequence.)