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Inference in Partially Linear Models under Dependent Data with Deep Neural Networks

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  • Chad Brown

Abstract

I consider inference in a partially linear regression model under stationary $\beta$-mixing data after first stage deep neural network (DNN) estimation. Using the DNN results of Brown (2024), I show that the estimator for the finite dimensional parameter, constructed using DNN-estimated nuisance components, achieves $\sqrt{n}$-consistency and asymptotic normality. By avoiding sample splitting, I address one of the key challenges in applying machine learning techniques to econometric models with dependent data. In a future version of this work, I plan to extend these results to obtain general conditions for semiparametric inference after DNN estimation of nuisance components, which will allow for considerations such as more efficient estimation procedures, and instrumental variable settings.

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  • Chad Brown, 2024. "Inference in Partially Linear Models under Dependent Data with Deep Neural Networks," Papers 2410.22574, arXiv.org.
    • Handle: RePEc:arx:papers:2410.22574
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    References listed on IDEAS

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    1. Max H. Farrell & Tengyuan Liang & Sanjog Misra, 2021. "Deep Neural Networks for Estimation and Inference," Econometrica, Econometric Society, vol. 89(1), pages 181-213, January.
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    7. Chad Brown, 2024. "Statistical Properties of Deep Neural Networks with Dependent Data," Papers 2410.11113, arXiv.org, revised Jan 2025.
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