Lectures 1 and 2 will be given on Monday September 29th, 2025, 4:30-7:30pm.
Lectures 3 and 4 will be given on Wednesday October 1st, 2025, 4:30-7:30pm.
Both courses will take place in room A01 in the Julis Romo Rabinowitz Building (JRRB).
While randomization-based inference with observational data has long been the subject of careful study in mathematical statistics, recent developments have made it increasingly relevant and impactful for applied work. This course presents classical and modern randomization-based inference methods through the prism of empirical analysis.
Lecture 1: Randomization Inference with Experimental vs Observational Data
The objective of this first lecture is twofold. First, we want to clarify and contrast in a crisp way the conditions and guarantees of exact tests on experimental and observational data. Second, we want to motivate randomization inference –and thus the upcoming lectures– as an inference tool that produces the desired inference in “placebo tests” and may be desirable in general, small sample applications.
Readings: Handout 1, Placebo Tests Done Right.
Lecture 2: Exact Tests Based on Invariance
We present general randomization inference theory for exact tests. We study how to choose or design a testing procedure such that the strong null delivering its exact validity is as plausible as possible in a given application.
Readings: Handout 2.
Lecture 3: Asymptotic Validity and Studentization
We present general randomization inference theory for asymptotic robustness of randomized tests. We detail the key role of studentization for asymptotic validity and explore how to studentize one's given test statistic in practice.
Readings: Handout 3, Romano (1990), Chung and Romano (2013).
Lecture 4: Linear Regression and Subvector Inference
Extending randomization inference to multivariate regression involves developing an exact test that will be invariant to the value of the regression coefficients not fixed under the null and that will be valid, at least asymptotically, under heteroskedasticity and model misspecification. We investigate the construction of such tests.
Readings: Handout 4, An Exact t -Test.
Lecture 5: Topics
We study modern topics in randomization inference and present some important theoretical and methodological open questions.