Optimal Data Acquisition for Statistical Estimation

TL;DR

This paper develops an optimal mechanism for data acquisition from strategic agents, minimizing worst-case estimation error under budget constraints, with applications to regression analysis.

Contribution

It introduces a closed-form optimal mechanism for data purchase that accounts for private costs and correlations, enhancing unbiased statistical estimation.

Findings

Design of an incentive-compatible, individually rational mechanism.

Characterization of the optimal mechanism in closed-form.

Extension to regression parameter estimation with correlated costs.

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.