'A bound for the error in the normal approximation to the distribution of a sum of dependent random variables'. Pp. 583-602 in: Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability. University of California, June 21-July 18, 1970. Volume II (2): Probability Theory.

First Edition. Frontisportrait (of William Feller), l, 605 pp. Original cloth. Very Good+, without dust jacket. 'Stein was certainly a most remarkable person. In 1956 he was 35 years old, a professor at Stanford University, which he had joined in 1953, and had already done some fundamental research in mathematical statistics, including the famous Hunt-Stein theorem relating group theory and statistical invariance. . . . he contributed a number of other important [results] to mathematical statistics. One of these was a 1972 paper in which he showed convergence in distribution to the normal and produced a Berry-Esseen type theorem for sums of dependent random variables. The technique he developed was quite novel and did not make use of Fourier methods, but relied instead on an elementary differential equation. His result, for example, gives a way of obtaining a Berry-Esseen result for U-statistics. Stein's result was applied in 1975 by Chen to the Poisson case and has since become known as the Chen-Stein method' ('Statistics in the Fifties', SASA's fiftieth anniversary conference presidential address). Other contributors include Debreu & Schmeidler, W. Hildenbrand, Kakutani, Gnedenko, et al. Also includes Mark Kac, 'William Feller, in Memoriam' (xxi-xxiii), L. K. Schmetterer, 'Alfréd Rényi, in Memoriam' (xxv-l).