Barbour A.D., Chen L.H.Y. Stein's Method and Applications

World Scientific, 2005. — 319 p.Stein's startling technique for deriving probability approximations first appeared about 30 years ago. Since then, much has been done to refine and develop the method, but it is still a highly active field of research, with many outstanding problems, both theoretical and in applications. This volume, the proceedings of a workshop held in honour of Charles Stein in Singapore, August 1983, contains contributions from many of the mathematicians at the forefront of this effort. It provides a cross-section of the work currently being undertaken, with many pointers to future directions. The papers in the collection include applications to the study of random binary search trees, Brownian motion on manifolds, Monte-Carlo integration, Edgeworth expansions, regenerative phenomena, the geometry of random point sets, and random matrices.Preface
Zero biasing in one and higher dimensions, and applications
Poisson limit theorems for the appearances of attributes
Normal approximation in geometric probability
Stein’s method, Edgeworth’s expansions and a formula of Barbour
Stein’s method for compound Poisson approximation via immigration–death processes
The central limit theorem for the independence number for minimal spanning trees in the unit square
Stein’s method, Markov renewal point processes, and strong memoryless times
Multivariate Poisson–binomial approximation using Stein’s method
An explicit Berry–Esseen bound for Student’s t-statistic via Stein’s method
An application of Stein’s method to maxima in hypercubes
Exact expectations of minimal spanning trees for graphs with random edge weights
Limit theorems for spectra of random matrices with martingale structure
Characterization of Brownian motion on manifolds through integration by parts
On the asymptotic distribution of some randomized quadrature rules
The permutation distribution of matrix correlation statistics
Applications of Stein’s method in the analysis of random binary search trees