## ABSTRACT

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.)