Chow, Y. S (1993). A moment inequality for Hsu and Robbins series. Vol.3, No.1.

Statistica Sinica 3(1993), 1-7

A MOMENT INEQUALITY FOR HSU AND

ROBBINS SERIES

Yuan S. Chow

National Central University and Columbia University

Abstract: The series involved in the Hsu and Robbins complete convergence theorem (1947) and its extensions by Katz (1963) and others are called Hsu and Robbins series. If p(|S_n|>2n) is replaced by nE(|S_n|-n)⁺ in the series, the new one is called the moment version of Hsu and Robbins series. We establish an inequality for such a series. Some results of Chow and Lai (1978) and Chow (1988) have been improved.

Key words and phrases: Moment inequality, complete convergence, Hsu and Robbins series.