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

arXiv: https://arxiv.org/abs/2410.22574 · HTML: https://mlsanity.com/paper/2410.22574/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 36 references that are in the map.
- First posted on arXiv 29 Oct 2024.

## Builds on (most cited first, 5 of 5)

- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [A vector-contraction inequality for Rademacher complexities](https://mlsanity.com/paper/1605.00251/) (2016)
- [Debiased Machine Learning without Sample-Splitting for Stable Estimators](https://mlsanity.com/paper/2206.01825/) (2022)
- [Statistical Properties of Deep Neural Networks with Dependent Data](https://mlsanity.com/paper/2410.11113/) (2024)
- [Simultaneous Inference of a Partially Linear Model in Time Series](https://mlsanity.com/paper/2212.10359/) (2022)

## Built on by (most cited first, 1 of 1)

- [Nonconvex Penalized LAD Estimation in Partial Linear Models with DNNs: Asymptotic Analysis and Proximal Algorithms](https://mlsanity.com/paper/2511.21115/) (2025)

## Abstract (arXiv)

I consider inference in a partially linear regression model under stationary β-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 √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.