Randomization Inference with Concentration Inequalities
Abstract
Randomization or design-based inference is becoming an increasingly popular tool for analysing data from randomized experiments: It does not require modelling assumptions on the distribution of outcomes or covariates, and hypothesis testing and estimation are respectively valid and unbiased in finite samples. Yet, confidence intervals for the sample average treatment effect (SATE) are still constructed via finite-population central limit theorems and their coverage is only asymptotic. In this work, we explore an alternative approach: We use concentration inequalities to construct confidence intervals for the SATE with non-asymptotic guarantees. We develop this approach for the most common experimental designs (Bernoulli trials and completely randomized experiments) and provide Hoeffding and Bernstein-type confidence intervals. Moreover, we extend these results to matched-pair, cluster and stratified randomized experiments. Our key technical contributions are a novel Bernstein-type concentration inequality for i.i.d. data points as well as a concentration result for Neyman's variance estimator.
Related
- Thermodynamic Concentration Inequalities: Controlling Uncertainty in Finite-Time and Small-Sample Thermodynamic Inference
- Randomization Inference: Theory and Applications
- Concentration inequalities for vector-valued martingales
- Majorization, Entropy and Concentration Inequalities for Discrete α-Concave Random Variables
- Selective Randomization Inference for Interference
BibTeX
@misc{freidling2026randomization,
title = {{Randomization Inference with Concentration Inequalities}},
author = {Tobias Freidling},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18586},
eprint = {2609.18586},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18586},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Randomization Inference with Concentration Inequalities
AU - Tobias Freidling
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18586
UR - https://arxiv.org/abs/2609.18586
AB - Randomization or design-based inference is becoming an increasingly popular tool for analysing data from randomized experiments: It does not require modelling assumptions on the distribution of outcomes or covariates, and hypothesis testing and estimation are respectively valid and unbiased in finite samples. Yet, confidence intervals for the sample average treatment effect (SATE) are still constructed via finite-population central limit theorems and their coverage is only asymptotic. In this work, we explore an alternative approach: We use concentration inequalities to construct confidence intervals for the SATE with non-asymptotic guarantees. We develop this approach for the most common experimental designs (Bernoulli trials and completely randomized experiments) and provide Hoeffding and Bernstein-type confidence intervals. Moreover, we extend these results to matched-pair, cluster and stratified randomized experiments. Our key technical contributions are a novel Bernstein-type concentration inequality for i.i.d. data points as well as a concentration result for Neyman's variance estimator.
ER -