Weak Moment Conditions Research Articles

Some more results on rates of convergence in the law of large numbers for weighted sums of independent random variables

are of interest in certain practical statistical and probabilistic problems. We have not attempted to provide a complete listing of the work done in this area. [1] through [11] contain several different types of current work, and provide a fairly large, though by no means complete, bibliography for this area. The results given here extend and sharpen the results of [6] giving rates of convergence of P{ISNI > e} to zero. There are five theorems in [6], each involving as a hypothesis some condition closely related to the existence of ElXk-EXklV. In the next section we extend and sharpen some of these theorems by considering separately the cases t?2 and t>2; in addition, we provide a theorem giving series convergence under weaker moment conditions than were used in [6] but under

Some results giving rates of convergence in the law of large numbers for weighted sums of independent random variables

are of interest in certain practical statistical and probabilistic problems. We have not attempted to provide a complete listing of the work done in this area. [1] through [11] contain several different types of current work, and provide a fairly large, though by no means complete, bibliography for this area. The results given here extend and sharpen the results of [6] giving rates of convergence of P{ISNI > e} to zero. There are five theorems in [6], each involving as a hypothesis some condition closely related to the existence of ElXk-EXklV. In the next section we extend and sharpen some of these theorems by considering separately the cases t?2 and t>2; in addition, we provide a theorem giving series convergence under weaker moment conditions than were used in [6] but under