arXiv 2 May 2025 · Statistics — Methodology
arXiv:2505.01324 · PDF · DOI · OpenAlex · Extracted main text
We introduce a design-based framework for causal inference that accommodates random potential outcomes, thereby extending the classical Neyman-Rubin model in which outcomes are treated as fixed. Each unit's potential outcome is modelled as a structural mapping $\tilde{y}_i(z, \omega)$, where $z$ denotes the treatment assignment and \(\omega\) represents latent outcome-level randomness. Inspired by recent connections between design-based inference and the Riesz representation theorem, we embed potential outcomes in a Hilbert space and define treatment effects as linear functionals, yielding estimators constructed via their Riesz representers. This approach preserves the core identification logic of randomised assignment while enabling valid inference under stochastic outcome variation. We establish large-sample properties under local dependence and develop consistent variance estimators that remain valid under weaker structural assumptions, including partially known dependence. A simulation study illustrates the robustness and finite-sample behaviour of the estimators. Overall, the framework unifies design-based reasoning with stochastic outcome modelling, broadening the scope of causal inference in complex experimental settings.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Harshaw, C., Y. Wang, and F. Sävje (2022) A design-based riesz representation framework for randomized experiments | 0.894 | 7 | 6 | 71% |
| 2 | Aronow, P. M. and C. Samii (2017) Estimating average causal effects under general interference | 0.843 | 3 | 3 | 100% |
| 3 | Ross, N (2011) Fundamentals of stein's method | 0.737 | 3 | 3 | 67% |
| 4 | Neyman, J (1990) On the application of probability theory to agricultural experiments. essay on principles. section 9 | 0.737 | 3 | 2 | 100% |
| 5 | Chernozhukov, V., W. K. Newey, R. Singh, and V. Syrgkanis (2025) Adversarial estimation of riesz representers | 0.511 | 2 | 2 | 50% |
| 6 | Adams, R. A. and J. J. F. Fournier (2003) Sobolev Spaces\/ (2nd ed.) | 0.511 | 2 | 2 | 50% |
| 7 | Billingsley, P (1999) Convergence of Probability Measures\/ (2nd ed.) | 0.511 | 2 | 2 | 50% |
| 8 | Chen, X (2007) Large sample sieve estimation of semi-nonparametric models | 0.511 | 2 | 2 | 50% |
| 9 | Chen, X. and D. Pouzo (2012) Estimation of nonparametric conditional moment models with possibly nonsmooth generalized residuals | 0.511 | 2 | 2 | 50% |
| 10 | van der Vaart, A. W (2000) Asymptotic statistics | 0.511 | 2 | 2 | 50% |
Showing the top 10 of 26 scored citations.