Randomization-based inference for distributions and quantiles of individual treatment effects

Chapter 1. Evaluating the treatment effect has become an important topic for many applications. However, most existing literature focuses mainly on average treatment effects. When the individual effects are heavy-tailed or have outlier values, not only may the average effect not be appropriate for summarizing treatment effects, but also the conventional inference for it can be sensitive and possibly invalid due to poor large-sample approximations. In this paper we focus on quantiles of individual treatment effects, which can be more robust in the presence of extreme individual effects. Moreover, our inference for them is purely randomization-based, avoiding any distributional assumptions on the units. We first consider inference in stratified randomized experiments, extending the recent work by Caughey et al. (2023). We show that the computation of valid p-values for testing null hypotheses on quantiles of individual effects can be transformed into instances of the multiple-choice knapsack problem, which can be efficiently solved exactly or slightly conservatively. We then extend our approach to matched observational studies and propose sensitivity analysis to investigate to what extent our inference on quantiles of individual effects is robust to unmeasured confounding. The proposed randomization inference and sensitivity analysis are simultaneously valid for all quantiles of individual effects, noting that the analysis for the maximum or minimum individual effect coincides with the conventional analysis assuming constant treatment effects. Chapter 2. Stochastic dominance is a fundamental concept that has been widely studied in econometrics and policy evaluation. In this paper, we propose a method for testing the null hypothesis that the sample distribution of individual treatment effects is first-order stochastically dominated by a prespecified distribution. This hypothesis can also be interpreted as a simultaneous test on the quantiles of individual effects. To achieve this, we design a class of Mann-Whitney U-statistics that reformulates the computation of valid p-values as an assignment problem, which can be efficiently solved using the Hungarian algorithm. Throughout the paper, we propose multiple methods to improve the power of the p-values. We further extend our approach to test the stochastic dominance of the population distribution of individual treatment effects, assuming that the observed units are randomly sampled from population with finite or infinite size.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois Urbana-Champaign

Year dc:date

2025

Author dc:creator

• Su, Yongchang

Contributors dc:contributor

• Li, Xinran
• Yu, Ruoqi
• Bowers, Jake
• Shao, Xiaofeng

• randomization inference
• sensitivity analysis
• multiple-choice knapsack problem
• greedy algorithm
• dynamic programming
• stochastic dominance

Statement dc:rights

• Copyright 2025 Yongchang Su

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/129509

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F129509