Asymptotic distributions and Berry-Esseen bounds for sums of record values

Let {U-n, n greater than or equal to 1} be independent uniformly distributed random variables, and {Y-n, n greater than or equal to 1} be independent and identically distributed non-negative random variables with finite third moments. Denote S-n = Sigma(i=1)(n) Y-i and assume that (U-1,...,U-n) and Sn+1, are independent for every fixed n. In this paper we obtain Berry-Esseen bounds for Sigma(i=1)(n)(UiSn+1), where psi is a non-negative function. As an application, we give Berry-Esseen bounds and asymptotic distributions for sums of record values.