Charles Stein, 1920-2016

Stein’s Method for the Bootstrap Dedicated to Charles Stein on the occasion of his 80th birthday

Stein’s method proves weak-convergence results through approximations to expectations without direct use of characteristic functions, allowing it to be used in complex problems with dependence. In this work we show how consistency can be proved and even some error terms provided for any bootstrap with exchangeable weights using Stein’s method. We say that the bootstrap works if the distance bet...

Stein E

We present a certain geometrical interpretation of the natural numbers, where these numbers appear as joint products of 5and 3-multiples located at specified positions in a revolving chamber. Numbers without factors 2, 3 or 5 appear at eight such positions, and any prime number larger than 7 manifests at one of these eight positions after a specified amount of rotations of the chamber. Our appr...

Stein Points

An important task in computational statistics and machine learning is to approximate a posterior distribution p(x) with an empirical measure supported on a set of representative points {xi}i=1. This paper focuses on methods where the selection of points is essentially deterministic, with an emphasis on achieving accurate approximation when n is small. To this end, we present Stein Points. The i...

Holomorphic fiber bundle with Stein base and Stein fibers

A surjective holomorphic map Π : X → Y between complex spaces is said to be a Stein morphism, if for every point y ∈ Y , there exists an open neighborhood U of y such that Π(U) is Stein. In 1977, Skoda [12] showed that a locally trivial analytic fiber bundle Π : X → Ω with Stein base and Stein fibers is not necessarily a Stein manifold. Thus giving a negative answer to a conjecture proposed in ...

Homer F. Swift, 1920