Tailoring Nuisance Function Estimation for Optimal Downstream Causal Inference

Researchers often aim to estimate causal effects using observational data. Modern causal inference methods increasingly rely on using nonparametric and/or high-dimensional machine learning methods to estimate nuisance functions such as the propensity score and conditional outcome mean. A standard pipeline involves estimating nuisance functions by minimizing their prediction errors (e.g., via cross-validation). In this talk, I consider the problem of how to tailor the estimation of nuisance functions for optimal downstream estimation of a target parameter that has gained prominence in the causal inference literature. I examine this problem through two regimes: nonparametric function classes and high-dimensional proportional asymptotics. I illustrate a delicate interplay between the optimal way to tune the estimation of nuisance functions, the type of estimator that uses these nuisance functions, and the sample splitting strategy. For each type of estimator and sample splitting strategy, I show that achieving optimal inference of the target parameter (e.g., minimax rate optimality, minimum asymptotic variance) often requires suboptimally estimating nuisance functions via undersmoothing or oversmoothing. I will conclude with a brief discussion of my related work on causal inference method development and applications for public health.

Co-Sponsored by the School of Public Health

Sean McGrath is a postdoctoral associate in the Department of Biostatistics at the Yale School of Public Health. His research focuses on statistical methods for causal inference and data integration studies with applications in public health and biomedical sciences. A secondary focus of his work is developing open-source software tools in these domains. Previously, he was a postdoctoral research fellow in the Department of Population Medicine at Harvard Medical School and Harvard Pilgrim Health Care Institute. He completed a PhD in Biostatistics at Harvard University, where he was supported by the National Science Foundation Graduate Research Fellowship.
 

This talk will also be available to watch live on Zoom.