Instance-Adaptive Hypothesis Tests with Heterogeneous Agents

TL;DR

This paper introduces a method for designing adaptive hypothesis tests for heterogeneous strategic agents, enabling near-oracle performance by eliciting private information through tailored menus of statistical contracts.

Contribution

It develops a framework for constructing instance-adaptive separating menus that match oracle performance without prior knowledge of agent types, linking statistical decision theory with mechanism design.

Findings

Separation menus can elicit private information cost-effectively.

Matching oracle performance is achievable without prior type knowledge.

Numerical examples demonstrate improved error trade-offs.

Abstract

We study hypothesis testing over a heterogeneous population of strategic agents with private information. Any single test applied uniformly across the population yields statistical error that is sub-optimal relative to the performance of an oracle given access to the private information. We show how it is possible to design menus of statistical contracts that pair type-optimal tests with payoff structures, inducing agents to self-select according to their private information. This separating menu elicits agent types and enables the principal to match the oracle performance even without a priori knowledge of the agent type. Our main result fully characterizes the collection of all separating menus that are instance-adaptive, matching oracle performance for an arbitrary population of heterogeneous agents. We identify designs where information elicitation is essentially costless, requiring negligible additional expense relative to a single-test benchmark, while improving statistical performance. Our work establishes a connection between proper scoring rules and menu design, showing how the structure of the hypothesis test constrains the elicitable information. Numerical examples illustrate the geometry of separating menus and the improvements they deliver in error trade-offs. Overall, our results connect statistical decision theory with mechanism design, demonstrating how heterogeneity and strategic participation can be harnessed to improve efficiency in hypothesis testing.