Date: 2024-02-29

Time: 14:00-15:00 (UK time)

Strand S5.20

Abstract

We study the estimation of partial derivatives of nonparametric regression functions with many variables, with a view to conducting a significance test for the said derivatives. Our test is based on the moment generating function of the smoothed partial derivatives of an estimator of the regression function, where the estimator is a deep neural network. We demonstrate that in the context of modelling with neural networks, derivative estimation is in fact quite different from estimating the regression function itself, and hence the smoothing operation becomes important. To conduct an effective test with predictors of high or even diverging dimension, we assume that first, the observed high-dimensional predictors arise from a factor model and that second, only the lower-dimensional but latent factors and a subset of the marginals of the high-dimensional predictors drive the regression function. Moreover, we finely adjust the regression function estimator in order to achieve the desired asymptotic normality under the null hypothesis that the partial derivative in question is zero. We demonstrate the performance of our test in simulation studies.

Speaker

Dr. Yue Zhao is a lecturer in statistics in the Department of Mathematics at the University of York. He obtained his PhD in statistics from Cornell University in 2015. His research interests lie in nonparametric and semiparametric multivariate dependence modelling (in particular, the copula) method, high-dimensional statistics, survival analysis and, more recently, statistical inference for neural networks.