Aronow, Peter M., Donald P. Green, and Donald K. K. Lee (2014). Sharp bounds on the variance in randomized experiments. The Annals of Statistics 42(3): 850--871. doi:10.1214/13-AOS1200.
We propose a consistent estimator of sharp bounds on the variance of the difference-in-means estimator in completely randomized experiments. Generalizing Robins [Stat. Med. 7 (1988) 773–785], our results resolve a well-known identification problem in causal inference posed by Neyman [Statist. Sci. 5 (1990) 465–472. Reprint of the original 1923 paper]. A practical implication of our results is that the upper bound estimator facilitates the asymptotically narrowest conservative Wald-type confidence intervals, with applications in randomized controlled and clinical trials.
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