The expressions for coverage probability and ASN of the Stein's two-stage confidence interval procedure for estimating the normal mean have been obtained under the assumption that the underlying distribution is, in fact, different from normal but could be approximated by the first four terms of Edgeworth series. The comparison of coverage probabilities with the corresponding probabilities obtained for the normal distribution shows that the procedure is quite insensitive to moderate departures from normality, and skewness of the parent population has very little effect on the coverage probability of the procedure. The Monte Carlo investigations which involve sampling from the gamma population confirm these conclusions.
"The Robustness of Stein's Two-Stage Procedure." Ann. Statist. 11 (4) 1251 - 1256, December, 1983. https://doi.org/10.1214/aos/1176346338