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

   
@article{EJP210,
	author = {Qi-Man Shao and Chun Su and Gang Wei},
	title = {Asymptotic Distributions and Berry-Esseen Bounds for Sums of Record Values},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {9},
	year = {2004},
	keywords = {},
	abstract = {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.},
	pages = {no. 17, 544-559},
	issn = {1083-6489},
	doi = {10.1214/EJP.v9-210},    
        url = {http://ejp.ejpecp.org/article/view/210}}