Dr. Ted Westling is an Assistant Professor of Statistics in the Department of Mathematics and Statistics at the University of Massachusetts Amherst. He received his PhD in Statistics from the University of Washington. He develops nonparametric theory and methods for problems in causal inference and survival analysis, with a focus on obtaining valid statistical inference when using machine learning. He is an expert in particular on causal inference with continuous exposures. He applies his research to public health, epidemiology, and biomedicine.
Talk: Debiased inference for a covariate-adjusted regression function
Abstract: 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. In particular, under certain causal conditions, this parameter corresponds to the average outcome had all units been assigned to a specific exposure level, known as the causal dose-response curve. 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 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.