Annals of Mathematical Statistics

Rates of Convergence for Weighted Sums of Random Variables

F. T. Wright

Full-text: Open access

Abstract

For $N = 1,2,\cdots$ let $S_N = \sum_k a_{N,k}X_k$ where $a_{N,k}$ is a real number for $N,k = 1,2, \cdots$ and $\{Xk\}$ is a sequence of not necessarily independent random variables. For the case $0 < t < 1$, with assumptions closely related to $E|X_k|^t < \infty$ it is shown that the rate of convergence of $P(|S_N| > \varepsilon)$ to zero is related to $\sum_k |a_{N,k}|^t$. The theorems presented here extend some of the results in the literature to not necessarily independent sequences $\{X_k\}$.

Article information

Source
Ann. Math. Statist., Volume 43, Number 5 (1972), 1687-1691.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177692403

Digital Object Identifier
doi:10.1214/aoms/1177692403

Mathematical Reviews number (MathSciNet)
MR348824

Zentralblatt MATH identifier
0251.60016

JSTOR
links.jstor.org

Citation

Wright, F. T. Rates of Convergence for Weighted Sums of Random Variables. Ann. Math. Statist. 43 (1972), no. 5, 1687--1691. doi:10.1214/aoms/1177692403. https://projecteuclid.org/euclid.aoms/1177692403


Export citation