Abstract
Let (W, W') be an exchangeable pair. Assume that
E(W − W'|W) = g(W) + r(W),
where g(W) is a dominated term and r(W) is negligible. Let G(t) = ∫0tg(s) ds and define p(t) = c1e−c0G(t), where c0 is a properly chosen constant and c1 = 1 / ∫−∞∞e−c0G(t) dt. Let Y be a random variable with the probability density function p. It is proved that W converges to Y in distribution when the conditional second moment of (W − W') given W satisfies a law of large numbers. A Berry–Esseen type bound is also given. We use this technique to obtain a Berry–Esseen error bound of order
Citation
Sourav Chatterjee. Qi-Man Shao. "Nonnormal approximation by Stein’s method of exchangeable pairs with application to the Curie–Weiss model." Ann. Appl. Probab. 21 (2) 464 - 483, April 2011. https://doi.org/10.1214/10-AAP712
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