Model-Assisted Uniformly Honest Inference for Optimal Treatment Regimes in High Dimension

Speaker：

Yunan Wu 吴宇楠

University of Texas at Dallas

I am an Assistant Professor at the University of Texas at Dallas, Mathematical Sciences. I obtained my PhD degree in University of Minnesota at n 2020, School of Statistics under the guidance of Prof. Lan Wang. After that, I joined Yale University, School of Public Health, Biostatistics as a Postdoc Associate, working with Prof. Hongyu Zhao. My main research interests are causal inference in precision medicine and Mendelian randomization, non-parametric and semi-parametric analysis, and high dimensional analysis. I am also interested studying incorrupted data and machine learning techniques.

摘要 Abstract：

We develop new tools to quantify uncertainty in optimal decision making and to gain insight into which variables one should collect information about given the potential cost of measuring a large number of variables. We investigate simultaneous inference to determine if a group of variables is relevant for estimating an optimal decision rule in a high-dimensional semiparametric framework. The unknown link function permits flexible modeling of the interactions between the treatment and the covariates but leads to nonconvex estimation in high dimension and imposes significant challenges for inference. We first establish that a local restricted strong convexity condition holds with high probability and that any feasible local sparse solution of the estimation problem can achieve the near-oracle estimation error bound. We verify that a wild bootstrap procedure based on a debiased version of the local solution can provide asymptotically honest uniform inference on optimal decision making.