Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/302890 
Year of Publication: 
2024
Series/Report no.: 
cemmap working paper No. CWP17/24
Publisher: 
Centre for Microdata Methods and Practice (cemmap), London
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 or more generally a set of variables. Our test statistics are based on the estimated partial derivative of the regression function of the candidate variable for screening and a 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 two real world applications.
Subjects: 
Neural networks
factor model
non-parametric regression
non-parametric tests
functional of derivatives
high-dimensionality
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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