Summary
Stein's method is used to derive asymptotic expansions for expectations of smooth functions of sums of independent random variables, together with Lyapounov estimates of the error in the approximation.
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Barbour, A.D. Asymptotic expansions based on smooth functions in the central limit theorem. Probab. Th. Rel. Fields 72, 289–303 (1986). https://doi.org/10.1007/BF00699108
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DOI: https://doi.org/10.1007/BF00699108