Discretized normal approximation by Stein’s method

Normal Approximation by Stein’s Method

The aim of this paper is to give an overview of Stein’s method, which has turned out to be a powerful tool for estimating the error in normal, Poisson and other approximations, especially for sums of dependent random variables. We focus on the normal approximation of random variables posessing decompositions of Barbour, Karoński, and Ruciński (1989), which are particularly useful in combinatori...

Stein’s method for normal approximation

Stein’s method originated in 1972 in a paper in the Proceedings of the Sixth Berkeley Symposium. In that paper, he introduced the method in order to determine the accuracy of the normal approximation to the distribution of a sum of dependent random variables satisfying a mixing condition. Since then, many developments have taken place, both in extending the method beyond normal approximation an...

Discretized Picard’s Method

Using the Modified Picard Method of Parker and Sochacki [1, 2], we derive a hybrid scheme using the analytical Picard method with approximations to the differential operators. This new method, called Discretized Picard’s Method, uses approximations in the space dimensions to compute derivatives but utilizes a continuous approximation in the time dimension. We illustrate the method using finite ...

A new method of normal approximation

We introduce a new version of Stein’s method that reduces a large class of normal approximation problems to variance bounding exercises, thus making a connection between central limit theorems and concentration of measure. Unlike Skorokhod embeddings, the object whose variance has to be bounded has an explicit formula that makes it possible to carry out the program more easily. As an applicatio...

Stein ’ s Method and Normal Approximation