# Optimal Data Acquisition for Statistical Estimation

arXiv: https://arxiv.org/abs/1711.01295 · HTML: https://mlsanity.com/paper/1711.01295/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2017.

## Built on by (most cited first, 9 of 9)

- [Optimal and Differentially Private Data Acquisition: Central and Local Mechanisms](https://mlsanity.com/paper/2201.03968/) (2022)
- [The Fair Value of Data Under Heterogeneous Privacy Constraints in Federated Learning](https://mlsanity.com/paper/2301.13336/) (2023)
- [Addressing Budget Allocation and Revenue Allocation in Data Market Environments Using an Adaptive Sampling Algorithm](https://mlsanity.com/paper/2306.02543/) (2023)
- [Optimal Scoring Rule Design under Partial Knowledge](https://mlsanity.com/paper/2107.07420/) (2021)
- [Striking a Balance: An Optimal Mechanism Design for Heterogenous Differentially Private Data Acquisition for Logistic Regression](https://mlsanity.com/paper/2309.10340/) (2023)
- [Trading-off price for data quality to achieve fair online allocation](https://mlsanity.com/paper/2306.13440/) (2023)
- [Learning from Biased and Costly Data Sources: Minimax-optimal Data Collection under a Budget](https://mlsanity.com/paper/2602.17894/) (2026)
- [Designing DSIC Mechanisms for Data Sharing in the Era of Large Language Models](https://mlsanity.com/paper/2506.05379/) (2025)
- [A Cram'er-von Mises Approach to Incentivizing Truthful Data Sharing](https://mlsanity.com/paper/2506.07272/) (2025)

## Abstract (arXiv)

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.