DMS Statistics and Data Science Seminar

Speaker: Dr. Shujie Ma (University of California at Riverside)

Title: Causal Inference on Quantile Dose-response Functions via Local ReLU Least Squares Weighting

Abstract: In this talk, I will introduce a novel local ReLU network least squares weighting method to estimate quantile dose-response functions in observational studies. Unlike the conventional inverse propensity weighting (IPW)  method, we estimate the weighting function involved in the treatment effect estimator directly through local ReLU least squares optimization. The proposed method takes advantage of ReLU networks applied for the baseline covariates with increasing dimension to alleviate the dimensionality problem while retaining flexibility and local kernel smoothing for the continuous treatment to precisely estimate the quantile dose-response function and prepare for statistical inference. Our method enjoys computational convenience, scalability, and flexibility. It also improves robustness and numerical stability compared to the conventional IPW method. We show that the ReLU networks can break the notorious `curse of dimensionality' when the weighting function belongs to a newly introduced smoothness class.  We also establish the convergence rate for the ReLU network estimator and the asymptotic normality of the proposed estimator for the quantile dose-response function. We further propose a multiplier bootstrap method to construct confidence bands for quantile dose-response functions. The finite sample performance of our proposed method is illustrated through simulations and a real data application.