Optimum Statistical Estimation with Strategic Data Sources

TL;DR

This paper introduces an optimal incentive mechanism for data sources in statistical estimation, balancing data quality and cost across various regression methods and objectives.

Contribution

It presents a general mechanism design framework for incentivizing data providers, optimizing estimation accuracy and cost in statistical models.

Findings

Mechanism minimizes combined payment and error costs.

Applicable to multiple regression techniques including ridge regression.

Framework extends to incentivize data labeling with cost considerations.

Abstract

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.