Weining Wang - University of Groningen

"Conditional nonparametric variable screening via deep neural network factor regression", with Jianqing Fan and Yue Zhao

Abstract

We propose a conditional screening test for non-parametricregression. To render our test effective when facing predictors with high or even diverging dimension, we assume that the observed predictors arise from a factor model where the factors are latent but lower-dimensional. Our test statistics are based on the estimated partial derivative in the screening variable when conditioning on the extracted proxies for the factors. Hence, our test reveals how much predictors contribute to non-parametric regression after accounting for the factors. Our derivative estimator is the convolution of a deep neural network regression function estimator and a smoothing kernel. We demonstrate that when the neural network could scale up as the sample size grows, unlike estimating the regression function itself, it is important to smooth the partial derivative of the neural network estimator to recover the desired convergence rate for the derivative. Moreover, our screening test achieves consistency for local alternatives under mild conditions, as well as asymptotic normality under the null after finely centering our test statistics. We demonstrate the performance of our test in a simulation study and two real world applications.

Additional information:

  • Speaker: Weining Wang
  • Time: Thursday, 04.07.2024, 11:00 - 12:00
  • Location: Faculty Lounge, Room 0.036
  • Further links:
  • Organizer: Statistics Group
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