Date: 2024-12-06
Time: 15:30-16:30 (Montreal time)
Location: In person, Burnside 1104
https://mcgill.zoom.us/j/83785721810
Meeting ID: 837 8572 1810
Passcode: None
Abstract:
High-dimensional covariates often admit linear factor structure. To effectively screen correlated covariates in high-dimension, we propose a conditional variable screening test based on non-parametric regression using neural networks due to their representation power. We ask the question whether individual covariates have additional contributions given the latent factors. Our test statistics are based on the estimated partial derivative of the regression function of the candidate variable for screening and an observable proxy for the latent factors. Hence, our test reveals how much predictors contribute additionally to the non-parametric regression after accounting for the latent factors. Our derivative estimator is the convolution of a deep neural network regression estimator and a smoothing kernel. We demonstrate that when the neural network size diverges with the sample size, unlike estimating the regression function itself, it is necessary to smooth the partial derivative of the neural network estimator to recover the desired convergence rate for the derivative. Moreover, our screening test achieves asymptotic normality under the null after finely centering our test statistics that makes the biases negligible, as well as consistency for local alternatives under mild conditions. We demonstrate the performance of our test in a simulation study and a real world application.
Speaker
Yue Zhao is an assistant professor at the University of York in the U.K. He received a Bachelor’s degree from Stanford University and Ph.D. degrees in physics and statistics from Princeton University and Cornell University respectively. He then worked as a postdoctoral researcher at McGill University and KU Leuven in Belgium before joining York in 2019. Yue Zhao is interested in the copula method, high-dimensional statistics, and applied empirical processes.