Zero Bias Enhanced Stein Couplings

TL;DR

This paper introduces zero bias enhanced Stein couplings, a flexible generalization that simplifies calculations and improves bounds in normal approximation, demonstrated through applications like the Lightbulb process.

Contribution

It extends Stein couplings to include zero bias versions, allowing for non-exact couplings and simplifying variance computations in normal approximation.

Findings

Improved bounds in normal approximation without complex variance calculations

Application to Lightbulb process showing better bounds than previous methods

Demonstrates the flexibility and effectiveness of zero bias Stein couplings

Abstract

The Stein couplings of Chen and Roellin (2010) vastly expanded the range of applications for which coupling constructions in Stein's method for normal approximation could be applied, and subsumed both Stein's classical exchangeable pair, as well as the size bias coupling. A further simple generalization includes zero bias couplings, and also allows for situations where the coupling is not exact. The zero bias versions result in bounds for which often tedious computations of a variance of a conditional expectation is not required. An example to the Lightbulb process shows that even though the method may be simple to apply, it may yield improvements over previous results that had achieved bounds with optimal rates and small, explicit constants.