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Published June 2018 | Published
Book Section - Chapter Open

Optimal Data Acquisition for Statistical Estimation

Abstract

We consider a data analyst's problem of purchasing data from strategic agents to compute an unbiased estimate of a statistic of interest. Agents incur private costs to reveal their data and the costs can be arbitrarily correlated with their data. Once revealed, data are verifiable. This paper focuses on linear unbiased estimators. We design an individually rational and incentive compatible mechanism that optimizes the worst-case mean-squared error of the estimation, where the worst-case is over the unknown correlation between costs and data, subject to a budget constraint in expectation. We characterize the form of the optimal mechanism in closed-form. We further extend our results to acquiring data for estimating a parameter in regression analysis, where private costs can correlate with the values of the dependent variable but not with the values of the independent variables.

Additional Information

© 2018 Copyright held by the owner/author(s). Publication rights licensed to ACM. Yiling Chen was partially supported by NSF grant CCF-1718549. Juba Ziani was supported by NSF grants CNS-1331343 and CNS-1518941, and the US-Israel Binational Science Foundation grant 2012348. Part of the work was done while Yiling Chen and Juba Ziani were at Microsoft Research New England.

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