Electronic Journal of Statistics

Confidence intervals for linear unbiased estimators under constrained dependence

Peter M. Aronow, Forrest W. Crawford, and José R. Zubizarreta

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We propose an approach for conducting inference for linear unbiased estimators applied to dependent outcomes given constraints on their independence relations, in the form of a dependency graph. We establish the consistency of an oracle variance estimator when a dependency graph is known, along with an associated central limit theorem. We derive an integer linear program for finding an upper bound for the estimated variance when a dependency graph is unknown, but topological or degree-based constraints are available on one such graph. We develop alternative bounds, including a closed-form bound, under an additional homoskedasticity assumption. We establish a basis for Wald-type confidence intervals that are guaranteed to have asymptotically conservative coverage.

Article information

Electron. J. Statist., Volume 12, Number 2 (2018), 2238-2252.

Received: December 2017
First available in Project Euclid: 23 July 2018

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Dependency graph oracle estimator variance estimate

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Aronow, Peter M.; Crawford, Forrest W.; Zubizarreta, José R. Confidence intervals for linear unbiased estimators under constrained dependence. Electron. J. Statist. 12 (2018), no. 2, 2238--2252. doi:10.1214/18-EJS1448. https://projecteuclid.org/euclid.ejs/1532333004

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