Moulinath Banerjee completed his Bachelor’s and Master’s in statistics at the Indian Statistical Institute in 1995 and 1997, respectively, then authored a doctoral dissertation, Likelihood Ratio Inference in Regular and Nonregular Problems in 2000, advised by Jon A. Wellner of the University of Washington. He remained in Washington as a lecturer until joining the University of Michigan faculty in 2001. His research interests comprise non-standard statistical models, shape-constrained methods, empirical process theory, distributed computing, learning across environments, and more recently, applications of OT at the statistics and machine learning interface. Apart from his statistical pursuits, he takes an avid interest in classical music, fine dining, literature, and philosophy, and together with a co-author has published a new translation of the Rubaiyat of Omar Khayyam from the original Persian. He is an elected fellow of both the ASA and the IMS, and the current editor of IMS’s review journal, Statistical Science.
This Medallion lecture will be delivered at the World Congress in Probability and Statistics in Bochum, Germany, in August: www.bernoulli-ims-worldcongress2024.org.

Estimation and inference for the average treatment effect in a score-explained heterogeneous treatment effect model
Non-randomized treatment effect models, in which the treatment assignment depends on (functions of) certain covariates being above or below some threshold, are widely used in fields like econometrics, political science, and epidemiology. Treatment effect estimation in such models is generally done using a local approach (e.g., RDD), which only considers observations from a small neighborhood of the threshold. In numerous situations, however, researchers are equally (or more) interested in individuals farther away from the threshold and the effect of treatment on such individuals. In this talk, we present a new method for estimating non-randomized heterogeneous treatment effects that consider all observations regardless of their distance from the threshold. The key idea is to model the `score’ of an individual based on which treatment is assigned as a function of measured covariates. We observe $(X, Y, Q)$ for each individual, where $X$ is the background covariates, $Y$ is the response variable, and $Q$ is the score.

To be more concrete, consider the example of estimating the effect of a scholarship on a student’s future performance. Here, $Y$ represents some measure of future performance, such as grades in college or university, future income, etc. The variable $X$ consists of some background information on the student (e.g., race, socio-economic status, etc.), and $Q$ denotes the score of the student on the scholarship test. We model the observations as follows:
\begin{align*}
Y_i & =\alpha_0(X_i, \eta_i)\mathbb{1}_{Q_i \ge \tau_0} + X_i^\top \beta_0 + \nu_i \\
Q_i &= X_i^\top \gamma_0 + \eta_i \,.
\end{align*}
where $\tau_0$ is the cutoff in the scholarship examination.
Our parameter of interest is the average treatment effect on treated (ATT), which is defined as:
$$
\theta_0 = \mathbb{E}[\alpha_0(X, \eta) \mid Q \ge \tau_0] \,.
$$

However, since both the response variable Y and performance in the scholarship examination Q depend on an unobserved confounder (e.g., a student’s innate ability), we do not assume
$(\eta, \nu)$ to be independent. Instead, they can be generated from any bivariate distribution.
We show that our method is capable of estimating ATT at a parametric rate irrespective of the correlation among the errors. We apply our method to simulated and real data sets, compare our results with those from existing approaches, and conclude with possible extensions of our method.