Open Access
2018 Confidence intervals for linear unbiased estimators under constrained dependence
Peter M. Aronow, Forrest W. Crawford, José R. Zubizarreta
Electron. J. Statist. 12(2): 2238-2252 (2018). DOI: 10.1214/18-EJS1448


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.


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Peter M. Aronow. Forrest W. Crawford. José R. Zubizarreta. "Confidence intervals for linear unbiased estimators under constrained dependence." Electron. J. Statist. 12 (2) 2238 - 2252, 2018.


Received: 1 December 2017; Published: 2018
First available in Project Euclid: 23 July 2018

zbMATH: 06917475
MathSciNet: MR3830833
Digital Object Identifier: 10.1214/18-EJS1448

Keywords: dependency graph , oracle estimator , Variance estimate

Vol.12 • No. 2 • 2018
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