Complete Moment and Integral Convergence for Sums of Negatively Associated Random Variables

For a sequence of identically distributed negatively associated random variables {X; n≥1} with partial sums S=(?)=1 X, n≥1, refinements are presented of the classical Baum-Katzand Lai complete convergence theorems. More specifically, necessary and sufficient moment conditionsare provided for complete moment convergence of the formto hold where r >1, q >0 and either no = 1,0 <p <2,a= 1,b= n or no = 3,p = 2, a=(log n), b= n log n. These results extend results of Chow and of Li and Spataru from the independentand identically distributed case to the identically distributed negatively associated setting. Thecomplete moment convergence is also shown to be equivalent to a form of complete integral convergence.