IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2402.14764.html
   My bibliography  Save this paper

A Combinatorial Central Limit Theorem for Stratified Randomization

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2402.14764
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fangzhou Su & Peng Ding, 2021. "Model‐assisted analyses of cluster‐randomized experiments," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(5), pages 994-1015, November.
    2. Zhao, Anqi & Ding, Peng, 2024. "No star is good news: A unified look at rerandomization based on p-values from covariate balance tests," Journal of Econometrics, Elsevier, vol. 241(1).
    3. Yuehao Bai & Azeem M. Shaikh & Max Tabord-Meehan, 2024. "A Primer on the Analysis of Randomized Experiments and a Survey of some Recent Advances," Papers 2405.03910, arXiv.org.
    4. Clément de Chaisemartin, 2022. "Trading-off Bias and Variance in Stratified Experiments and in Staggered Adoption Designs, Under a Boundedness Condition on the Magnitude of the Treatment Effect," Working Papers hal-03873919, HAL.
    5. Han, Kevin & Basse, Guillaume & Bojinov, Iavor, 2024. "Population interference in panel experiments," Journal of Econometrics, Elsevier, vol. 238(1).
    6. Purevdorj Tuvaandorj, 2021. "Robust Permutation Tests in Linear Instrumental Variables Regression," Papers 2111.13774, arXiv.org, revised Jul 2024.
    7. Peter Z. Schochet, 2018. "Design-Based Estimators for Average Treatment Effects for Multi-Armed RCTs," Journal of Educational and Behavioral Statistics, , vol. 43(5), pages 568-593, October.
    8. Peter Ganong & Simon Jäger, 2018. "A Permutation Test for the Regression Kink Design," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 494-504, April.
    9. Iavor Bojinov & David Simchi-Levi & Jinglong Zhao, 2023. "Design and Analysis of Switchback Experiments," Management Science, INFORMS, vol. 69(7), pages 3759-3777, July.
    10. Rauf Ahmad & Per Johansson & Mårten Schultzberg, 2024. "Is Fisher inference inferior to Neyman inference for policy analysis?," Statistical Papers, Springer, vol. 65(6), pages 3425-3445, August.
    11. Bai, Yuehao & Jiang, Liang & Romano, Joseph P. & Shaikh, Azeem M. & Zhang, Yichong, 2024. "Covariate adjustment in experiments with matched pairs," Journal of Econometrics, Elsevier, vol. 241(1).
    12. Jiafeng Chen, 2021. "Nonparametric Treatment Effect Identification in School Choice," Papers 2112.03872, arXiv.org, revised Oct 2023.
    13. Peter Z. Schochet, 2020. "Analyzing Grouped Administrative Data for RCTs Using Design-Based Methods," Journal of Educational and Behavioral Statistics, , vol. 45(1), pages 32-57, February.
    14. Haoge Chang, 2023. "Design-based Estimation Theory for Complex Experiments," Papers 2311.06891, arXiv.org.
    15. Iavor Bojinov & Ashesh Rambachan & Neil Shephard, 2021. "Panel experiments and dynamic causal effects: A finite population perspective," Quantitative Economics, Econometric Society, vol. 12(4), pages 1171-1196, November.
    16. Hyunseung Kang & Laura Peck & Luke Keele, 2018. "Inference for instrumental variables: a randomization inference approach," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 1231-1254, October.
    17. Yuehao Bai, 2022. "Optimality of Matched-Pair Designs in Randomized Controlled Trials," Papers 2206.07845, arXiv.org.
    18. Peter L. Cohen & Colin B. Fogarty, 2022. "Gaussian prepivoting for finite population causal inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 295-320, April.
    19. Eduardo Fé, 2021. "Pension eligibility rules and the local causal effect of retirement on cognitive functioning," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(3), pages 812-841, July.
    20. Nicole E. Pashley & Luke W. Miratrix, 2021. "Insights on Variance Estimation for Blocked and Matched Pairs Designs," Journal of Educational and Behavioral Statistics, , vol. 46(3), pages 271-296, June.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2402.14764. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.