Berry-Esseen Bounds for Random Index Non Linear Statistics via Stein's Method

Under the second moment condition, we obtain Berry-Esseen bounds for random index non linear statistics by using a technique discussed in Chen and Shao (2007 Chen, L. H.Y., Shao, Q.-M. (2007). Normal approximation for nonlinear statistics using a concentration inequality approach. Bernoulli 13(2):581–599.[Crossref], [Web of Science ®] , [Google Scholar]). A concept in this article is to approximate any random index non-linear statistic by a random index linear statistic. The bounds for random sums of independent random variables are also provided. Applications are the bounds for random U-statistics and random sums of the present values in investment analysis.