# Optimum Statistical Estimation with Strategic Data Sources

arXiv: https://arxiv.org/abs/1408.2539 · HTML: https://mlsanity.com/paper/1408.2539/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Aug 2014.

## Built on by (most cited first, 28 of 28)

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- [Information Discrepancy in Strategic Learning](https://mlsanity.com/paper/2103.01028/) (2021)
- [Strategic Instrumental Variable Regression: Recovering Causal Relationships From Strategic Responses](https://mlsanity.com/paper/2107.05762/) (2021)
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- [Learning When to Advise Human Decision Makers](https://mlsanity.com/paper/2209.13578/) (2022)
- [How and Why to Manipulate Your Own Agent: On the Incentives of Users of Learning Agents](https://mlsanity.com/paper/2112.07640/) (2021)
- [An Equivalence Between Data Poisoning and Byzantine Gradient Attacks](https://mlsanity.com/paper/2202.08578/) (2022)
- [Delegated Classification](https://mlsanity.com/paper/2306.11475/) (2023)
- [Delegating Data Collection in Decentralized Machine Learning](https://mlsanity.com/paper/2309.01837/) (2023)
- [Online covariance estimation for stochastic gradient descent under Markovian sampling](https://mlsanity.com/paper/2308.01481/) (2023)
- [Constrained Stochastic Nonconvex Optimization with State-dependent Markov Data](https://mlsanity.com/paper/2206.11346/) (2022)
- [Incentivizing Honesty among Competitors in Collaborative Learning and Optimization](https://mlsanity.com/paper/2305.16272/) (2023)
- [SelectMix: Enhancing Label Noise Robustness through Targeted Sample Mixing](https://mlsanity.com/paper/2509.11265/) (2025)
- [Optimal Scoring Rule Design under Partial Knowledge](https://mlsanity.com/paper/2107.07420/) (2021)
- [Truthful Incentive Mechanism for Federated Learning with Crowdsourced Data Labeling](https://mlsanity.com/paper/2302.00106/) (2023)
- [Collaborative Mean Estimation Among Heterogeneous Strategic Agents: Individual Rationality, Fairness, and Truthful Contribution](https://mlsanity.com/paper/2407.15881/) (2024)
- [Striking a Balance: An Optimal Mechanism Design for Heterogenous Differentially Private Data Acquisition for Logistic Regression](https://mlsanity.com/paper/2309.10340/) (2023)
- [Auctions and Peer Prediction for Academic Peer Review](https://mlsanity.com/paper/2109.00923/) (2021)
- [Metric-Fair Classifier Derandomization](https://mlsanity.com/paper/2206.07826/) (2022)
- [Strategyproof Learning: Building Trustworthy User-Generated Datasets](https://mlsanity.com/paper/2106.02398/) (2021)
- [Long-term Data Sharing under Exclusivity Attacks](https://mlsanity.com/paper/2201.09137/) (2022)
- [Truthful Generalized Linear Models](https://mlsanity.com/paper/2209.07815/) (2022)
- [No Bidding, No Regret: Pairwise-Feedback Mechanisms for Digital Goods and Data Auctions](https://mlsanity.com/paper/2306.01860/) (2023)
- [Incentivizing High-Quality Human Annotations with Golden Questions](https://mlsanity.com/paper/2505.19134/) (2025)
- [A Cram'er-von Mises Approach to Incentivizing Truthful Data Sharing](https://mlsanity.com/paper/2506.07272/) (2025)
- [Users as Annotators: LLM Preference Learning from Comparison Mode](https://mlsanity.com/paper/2510.13830/) (2025)
- [Gradient Manipulation in Distributed Stochastic Gradient Descent with Strategic Agents: Truthful Incentives with Convergence Guarantees](https://mlsanity.com/paper/2603.27962/) (2026)

## Abstract (arXiv)

We propose an optimum mechanism for providing monetary incentives to the data sources of a statistical estimator such as linear regression, so that high quality data is provided at low cost, in the sense that the sum of payments and estimation error is minimized. The mechanism applies to a broad range of estimators, including linear and polynomial regression, kernel regression, and, under some additional assumptions, ridge regression. It also generalizes to several objectives, including minimizing estimation error subject to budget constraints. Besides our concrete results for regression problems, we contribute a mechanism design framework through which to design and analyze statistical estimators whose examples are supplied by workers with cost for labeling said examples.