The Annals of Statistics

Sharp bounds on the variance in randomized experiments

Peter M. Aronow, Donald P. Green, and Donald K. K. Lee

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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.

Article information

Ann. Statist. Volume 42, Number 3 (2014), 850-871.

First available in Project Euclid: 20 May 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62A01: Foundations and philosophical topics
Secondary: 62D99: None of the above, but in this section 62G15: Tolerance and confidence regions

Causal inference finite populations potential outcomes randomized experiments variance estimation


Aronow, Peter M.; Green, Donald P.; Lee, Donald K. K. Sharp bounds on the variance in randomized experiments. Ann. Statist. 42 (2014), no. 3, 850--871. doi:10.1214/13-AOS1200.

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