A note on the exchangeability condition in Stein's method

Details A note on the exchangeability condition in Stein's method A note on the exchangeability condition in Stein's method

2006-11-02

arxiv.org/abs/math/0611050v2

Mathematics

Probability

Scientific paper

10.1016/j.spl.2008.01.043

We show by a surprisingly simple argument that the exchangeability condition, which is key to the exchangeable pair approach in Stein's method for distributional approximation, can be omitted in many standard settings. This is achieved by replacing the usual antisymmetric function by a simpler one, for which only equality in distribution is required. In the case of normal approximation we also slightly improve the constants appearing in previous results. For Poisson approximation, a different antisymmetric function is used, and additional error terms are needed if the bound is to be extended beyond the exchangeable setting.

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