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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.
    2. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    3. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    4. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    5. Chad Brown, 2024. "Statistical Properties of Deep Neural Networks with Dependent Data," Papers 2410.11113, arXiv.org, revised Nov 2024.
    6. Qizhao Chen & Vasilis Syrgkanis & Morgane Austern, 2022. "Debiased Machine Learning without Sample-Splitting for Stable Estimators," Papers 2206.01825, arXiv.org, revised Nov 2022.
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