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A Combinatorial Central Limit Theorem for Stratified Randomization

Purevdorj Tuvaandorj

arXiv 22 Feb 2024 · Mathematics — Statistics Theory

arXiv:2402.14764 · PDF · DOI · OpenAlex · Extracted main text

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.

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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1D'Haultfuille, X. and P. Tuvaandorj (2024) A Robust Permutation Test for Subvector Inference in Linear Regressions0.92843100%
2Andrews, D. W. K. and V. Marmer (2008) Exactly Distribution-Free Inference in Instrumental Variables Regression with Possibly Weak Instruments0.874112100%
3Imbens, G. W. and P. R. Rosenbaum (2005) Robust, Accurate Confidence Intervals with a Weak Instrument: Quarter of Birth and Education0.87492100%
4Liu, H. and Y. Yang (2020) Regression-Adjusted Average Treatment Effect Estimates in Stratified Randomized Experiments0.81142100%
5Bolthausen, E (1984) An Estimate of the Remainder in a Combinatorial Central Limit Theorem0.7374350%
6Schneller, W (1988) A Short Proof of Motoo's Combinatorial Central Limit Theorem using Stein's Method0.7373367%
7Hoeffding, W. (1951, 12) (1951) A Combinatorial Central Limit Theorem0.73732100%
8Li, X. and P. Ding (2017) General Forms of Finite Population Central Limit Theorems with Applications to Causal Inference0.73732100%
9Bickel, P. J. and D. A. Freedman (1984) Asymptotic Normality and the Bootstrap in Stratified Sampling0.58531100%
10van der Vaart, A. W (1998) Asymptotic Statistics0.5112250%

Showing the top 10 of 31 scored citations.