A0919
Title: Method-of-moments inference for GLMs and doubly robust functionals under proportional asymptotics
Authors: Rajarshi Mukherjee - Harvard T.H. Chan School of Public Health (United States) [presenting]
Abstract: The purpose is to consider the estimation of regression coefficients and signal-to-noise (SNR) ratio in high-dimensional generalized linear models (GLMs) and explore their implications in inferring popular estimands, such as average treatment effects in high-dimensional observational studies. Under the "proportional asymptotic'' regime and Gaussian covariates with known (population) covariance (Sigma), root-n-consistent and asymptotically normal (CAN) estimators of the targets of inference are derived through a method-of-moments type of estimators that bypasses estimation of high dimensional nuisance functions and hyperparameter tuning altogether. Additionally, under non-Gaussian covariates, the universality of the results is demonstrated under certain additional assumptions on the regression coefficients and Sigma. It is also demonstrated that knowing Sigma can be relaxed in the proposed methodology. Finally, the theoretical results are complemented with extensive numerical experiments in comparison with competing methods.
