Variable Selection for Partially Linear Models and Partially Global Fréchet Regression

Speaker: Yichao Wu, The University of Illinois at Chicago

Title: Variable Selection for Partially Linear Models and Partially Global Fréchet Regression

Abstract:

The first part of the talk will focus on the general partially linear model without any structure assumption on the nonparametric component. For such a model with both linear and nonlinear predictors being multivariate, we propose a new variable selection method. Our new method is a unified approach in the sense that it can select both linear and nonlinear predictors simultaneously by solving a single optimization problem. We prove that the proposed method achieves consistency.
The second part of the talk will be based on an ongoing research project. In this project, we are extending the above variable selection method to partially global Fréchet regression (Tucker and Wu, 2025 Statistica Sinica).