Electronic Journal of Probability

Asymptotic Distributions and Berry-Esseen Bounds for Sums of Record Values

Qi-Man Shao, Chun Su, and Gang Wei

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Let $\{U_n, n \geq 1\}$ be independent uniformly distributed random variables, and $\{Y_n, n \geq 1\}$ be independent and identically distributed non-negative random variables with finite third moments. Denote $S_n = \sum_{i=1}^n Y_i$ and assume that $ (U_1, \cdots, U_n)$ and $S_{n+1}$ are independent for every fixed $n$. In this paper we obtain Berry-Esseen bounds for $\sum_{i=1}^n \psi(U_i S_{n+1})$, where $\psi$ is a non-negative function. As an application, we give Berry-Esseen bounds and asymptotic distributions for sums of record values.

Article information

Electron. J. Probab., Volume 9 (2004), paper no. 17, 544-559.

Accepted: 9 June 2004
First available in Project Euclid: 6 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F10: Large deviations
Secondary: 60F15: Strong theorems

This work is licensed under aCreative Commons Attribution 3.0 License.


Shao, Qi-Man; Su, Chun; Wei, Gang. Asymptotic Distributions and Berry-Esseen Bounds for Sums of Record Values. Electron. J. Probab. 9 (2004), paper no. 17, 544--559. doi:10.1214/EJP.v9-210. https://projecteuclid.org/euclid.ejp/1465229703

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