Rates of convergence to normality for samples from a finite set of random variables
R. D. John, John Robinson · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1996
Abstract Rates of convergence to normality ofO(N-½) are obtained for a standardized sum ofmrandom variables selected at random from a finite set ofNrandom variables in two cases. In the first case, the sum is randomly normed and the variables are not restricted to being independent. The second case is an alternative proof of a result due to von Bahr, which deals with independent variables. Both results derive from a rate obtained by Höglund in the case of sampling from a finite population.