On normal approximation rates for certain sums of dependent random variables (Q1891021)

One of the difficulties in applying Stein's method for normal approximation is that the error estimates obtained are most naturally expressed in terms of a Wasserstein distance, and conversion to Kolmogorov distance with the same rate is usually difficult. A delicate analysis of the error terms arising in \textit{Ch. Stein}'s argument [``Approximate computation of expectations'' (1986; Zbl 0721.60016)] enables a Kolmogorov bound of the natural order to be obtained for sums of bounded random variables with a reasonably local dependency graph. All sorts of counts arising from Bernoulli random graphs can be treated using the result.