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A Combinatorial Central Limit Theorem for Stratified Randomization

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  • Purevdorj Tuvaandorj

Abstract

This paper establishes a combinatorial central limit theorem for stratified randomization, which holds under a Lindeberg-type condition. The theorem allows for an arbitrary number or sizes of strata, with the sole requirement being that each stratum contains at least two units. This flexibility accommodates both a growing number of large and small strata simultaneously, while imposing minimal conditions. We then apply this result to derive the asymptotic distributions of two test statistics proposed for instrumental variables settings in the presence of potentially many strata of unrestricted sizes.

Suggested Citation

  • Purevdorj Tuvaandorj, 2024. "A Combinatorial Central Limit Theorem for Stratified Randomization," Papers 2402.14764, arXiv.org, revised Apr 2024.
    • Handle: RePEc:arx:papers:2402.14764
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    References listed on IDEAS

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    1. Andrews, Donald W.K. & Marmer, Vadim, 2008. "Exactly distribution-free inference in instrumental variables regression with possibly weak instruments," Journal of Econometrics, Elsevier, vol. 142(1), pages 183-200, January.
    2. Guido W. Imbens & Paul R. Rosenbaum, 2005. "Robust, accurate confidence intervals with a weak instrument: quarter of birth and education," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(1), pages 109-126, January.
    3. Zhao, Anqi & Ding, Peng, 2021. "Covariate-adjusted Fisher randomization tests for the average treatment effect," Journal of Econometrics, Elsevier, vol. 225(2), pages 278-294.
    4. Xinran Li & Peng Ding, 2017. "General Forms of Finite Population Central Limit Theorems with Applications to Causal Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1759-1769, October.
    5. Colin B. Fogarty, 2018. "On mitigating the analytical limitations of finely stratified experiments," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(5), pages 1035-1056, November.
    6. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881.
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