## Annals of Mathematical Statistics

### Rates of Convergence for Weighted Sums of Random Variables

F. T. Wright

#### 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

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