arXiv 22 Feb 2024 · Mathematics — Statistics Theory
arXiv:2402.14764 · PDF · DOI · OpenAlex · Extracted main text
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.
appendix boundary found by appendix_command · 44% of the source is main text. Read the extracted text to check this.
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 | D'Haultfuille, X. and P. Tuvaandorj (2024) A Robust Permutation Test for Subvector Inference in Linear Regressions | 0.928 | 4 | 3 | 100% |
| 2 | Andrews, D. W. K. and V. Marmer (2008) Exactly Distribution-Free Inference in Instrumental Variables Regression with Possibly Weak Instruments | 0.874 | 11 | 2 | 100% |
| 3 | Imbens, G. W. and P. R. Rosenbaum (2005) Robust, Accurate Confidence Intervals with a Weak Instrument: Quarter of Birth and Education | 0.874 | 9 | 2 | 100% |
| 4 | Liu, H. and Y. Yang (2020) Regression-Adjusted Average Treatment Effect Estimates in Stratified Randomized Experiments | 0.811 | 4 | 2 | 100% |
| 5 | Bolthausen, E (1984) An Estimate of the Remainder in a Combinatorial Central Limit Theorem | 0.737 | 4 | 3 | 50% |
| 6 | Schneller, W (1988) A Short Proof of Motoo's Combinatorial Central Limit Theorem using Stein's Method | 0.737 | 3 | 3 | 67% |
| 7 | Hoeffding, W. (1951, 12) (1951) A Combinatorial Central Limit Theorem | 0.737 | 3 | 2 | 100% |
| 8 | Li, X. and P. Ding (2017) General Forms of Finite Population Central Limit Theorems with Applications to Causal Inference | 0.737 | 3 | 2 | 100% |
| 9 | Bickel, P. J. and D. A. Freedman (1984) Asymptotic Normality and the Bootstrap in Stratified Sampling | 0.585 | 3 | 1 | 100% |
| 10 | van der Vaart, A. W (1998) Asymptotic Statistics | 0.511 | 2 | 2 | 50% |
Showing the top 10 of 31 scored citations.