Inference for ATE & GLM’s when p/n→δ∈(0,∞)

Abstract
In this talk we will discuss statistical inference of average treatment effect in measured confounder settings as well as parallel questions of inferring linear and quadratic functionals in generalized linear models under high dimensional proportional asymptotic settings i.e. when p/n→δ∈(0,∞) where p, n denote the dimension of the covariates and the sample size respectively . The results rely on the knowledge of the variance covariance matrix Σ of the covariates under study and we show that whereas √n-consistent asymptotically normal inference is possible for any δ by using method of moments type estimators that do not rely on estimating high dimensional nuisance parameters followed by a debiasing strategy. Without the knowledge of Σ we first develop √n-consistent estimators by using simple estimators of  Σ when δ < 1. Subsequently for δ ≥ 1, we develop consistent estimators of the quantities of interest and argue that √n-consistent estimation might not be possible without further assumptions on Σ. Finally we verify our results in numerical simulations. This talk is based on joint work with Xingyu Chen and Lin Liu from Shanghai Jiao Tong University.

Bio
Rajarshi Mukherjee is an Associate Professor in the Department of Biostatistics at Harvard T.H. Chan School of Public Health. Previously, he was an Assistant Professor in the Division of Biostatistics at UC Berkeley following his time as a Stein Fellow in the Department of Statistics at Stanford University. He obtained his PhD in Biostatistics from Harvard University, advised by Prof. Xihong Lin.

He is generally interested in understanding broad aspects of causal inference in observational studies in modern data settings with a focus on learning about fundamental challenges in the statistical analysis of environmental mixtures and their effects on the cognitive development of children and cogntitive decline in aging populations. His research is also motivated by learning through applications in large-scale genetic association studies, developing statistical methods to quantify the effects of climate change on human health, and understanding the effects of homelessness on human health.