## Annals of Mathematical Statistics

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

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

#### 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