SHARP BOUNDS ON THE VARIANCE IN RANDOMIZED EXPERIMENTS

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 wellknown identification problem in causal inference posed by Neyman [Statist. Sci. 5 (1990) 465-72. 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.