Zero bias enhanced Stein couplings

Abstract

The Stein couplings of Chen and Roellin [6] 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.