**Speaker:** Dr. Yuexiao Dong from Temple University

**Date and Time:** Friday, February 4, 2022, 11:00-12:00 via Zoom. Please contact Will Brian to obtain the Zoom link.

**Title:** Testing the linear mean and constant variance conditions in sufficient dimension reduction

**Abstract:** Sufficient dimension reduction (SDR) methods characterize the relationship between the response and the predictors through a few linear combinations of the predictors. Sliced inverse regression and sliced average variance estimation are among the most popular SDR methods as they do not involve multi-dimensional smoothing and are easy to implement. However, these inverse regression-based methods require the linear conditional mean (LCM) and(or) the constant conditional variance (CCV) assumption. We propose novel tests to check the validity of the LCM and the CCV conditions through the martingale difference divergence. Extensive simulation studies and a real data application are performed to demonstrate the effectiveness of our proposed tests.