Feasibility and variance costs in two-treated experiments with uncertain partners
Year: 2026
Type: article
Abstract: An evaluator can assign support to two participants in a paired task, yet receive only a list of possible pair rosters. Can one estimator recover the mean response under treatment of both a participant and their partner? For an even roster of at least four participants and a uniform draw of two treated units, a common linear unbiased estimator exists exactly when every participant has someone who is their partner in none of the candidate perfect matchings. In a four-unit example all units have zero common target support and the signed estimator is unique. Under the uniform design its worst variance over responses in [-M,M] is 9M^2, compared with 3M^2 for a linear unbiased estimator with the true matching revealed. For arbitrary positive treated-pair probabilities, the exact known-matching risk uses the inverse probabilities of its two edges, while the common estimator uses all six. The finite affine criterion specializes the established design-based Riesz framework. A proposed roster and assignment protocol specifies the inputs needed to apply these calculations. AI tools assisted with mathematical derivation, proof checking, literature comparison, and manuscript preparation.
Author: Xu, Zihuan
Institution: Capital Normal University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223865090