We study nonparametric inference for a covariate-adjusted regression function. This parameter captures the average association between a continuous exposure and an outcome after adjusting for other covariates. Under certain causal conditions, it also corresponds to the average outcome had all units been assigned to a specific exposure level, known as the causal dose-response curve. Building on Calonico et al. (2018), we propose a debiased local linear estimator of the covariate-adjusted regression function and demonstrate that our estimator converges pointwise to a mean-zero normal limit distribution. We use this result to construct asymptotically valid confidence intervals for function values and differences thereof. In addition, we use approximation results for the distribution of the supremum of an empirical process to construct asymptotically valid uniform confidence bands. Our methods do not require undersmoothing, permit the use of data-adaptive estimators of nuisance functions, and our estimator attains the optimal rate of convergence for a twice differentiable regression function. We illustrate the practical performance of our estimator using numerical studies and an analysis of the effect of air pollution exposure on cardiovascular mortality. This is joint work with Kenta Takatsu.
Bio: Ted Westling is an Assistant Professor of Statistics at University of Massachusetts Amherst. He received his PhD in Statistics in 2018 from the University of Washington, advised by Marco Carone. His research focuses on theory and methodology of nonparametric and shape-constrained statistics, often applied to problems in causal inference and survival analysis. A major focus of his work is achieving valid statistical inference when using machine learning as part of the estimation procedure.