Jianqing Fan, Weining Wang, Yue Zhao
arXiv 20 Aug 2024 · Econometrics
arXiv:2408.10825 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Fan, J. and Gu, Y (2023) Factor augmented sparse throughput deep ReLU neural networks for high dimensional regression self | 0.822 | 18 | 5 | 56% |
| 2 | Kohler, M. and Langer, S (2021) On the rate of convergence of fully connected deep neural network regression estimates | 0.737 | 4 | 4 | 50% |
| 3 | Fan, J. and Liao, Y (2022) Learning latent factors from diversified projections and its applications to over-estimated and weak factors self | 0.737 | 3 | 3 | 67% |
| 4 | Schmidt-Hieber, J (2020) Nonparametric regression using deep neural networks with ReLU activation function | 0.737 | 3 | 3 | 67% |
| 5 | Goodfellow, I., Bengio, Y., and Courville, A (2016) Deep Learning | 0.644 | 2 | 2 | 100% |
| 6 | McCracken, M. W. and Ng, S (2016) FRED-MD: A monthly database for macroeconomic research | 0.585 | 3 | 1 | 100% |
| 7 | Anthony, M. and Bartlett, P. L (1999) Neural Network Learning: Theoretical Foundations | 0.511 | 5 | 2 | 20% |
| 8 | Yarotsky, D (2017) Error bounds for approximations with deep ReLU networks | 0.511 | 4 | 2 | 25% |
| 9 | Conway, J. B (1990) A Course in Functional Analysis | 0.511 | 2 | 2 | 50% |
| 10 | Gasser, T. and Müller, H.-G (1984) Estimating regression functions and their derivatives by the kernel method | 0.511 | 2 | 2 | 50% |
Showing the top 10 of 73 scored citations.