YSPH Biostatistics Seminar: “Nuisance Function Tuning and Sample Splitting for Optimal Doubly Robust Estimation"

NOTE: BIS 525 students are required to attend in person. Others are invited to attend in person, but may also attend via Zoom.

SPEAKER: Sean McGrath, PhD, Postdoctoral Associate, Department of Biostatistics, Yale University

TITLE: “Nuisance Function Tuning and Sample Splitting for Optimal Doubly Robust Estimation"

ABSTRACT: Estimators of doubly robust functionals typically rely on estimating two complex nuisance functions, such as the propensity score and conditional outcome mean for the average treatment effect functional. We consider the problem of how to estimate nuisance functions to obtain optimal rates of convergence for a doubly robust nonparametric functional that has witnessed applications across the causal inference and conditional independence testing literature. For several plug-in estimators and a first-order bias-corrected estimator, we illustrate the interplay between different tuning parameter choices for the nuisance function estimators and sample splitting strategies on the optimal rate of estimating the functional of interest. For each of these estimators and each sample splitting strategy, we show the necessity to either undersmooth or oversmooth the nuisance function estimators under low regularity conditions to obtain optimal rates of convergence for the functional of interest. Unlike the existing literature, we show that plug-in and first-order bias-corrected estimators can achieve minimax rates of convergence across all Hölder smoothness classes of the nuisance functions by careful combinations of sample splitting and nuisance function tuning strategies.

YSPH values inclusion and access for all participants. If you have questions about accessibility or would like to request an accommodation, please contact Charmila Fernandes at Charmila.fernandes@yale.edu. We will try to provide accommodations requested by September 4, 2025.