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

TL;DR

This paper develops a method for conducting inference in partially linear models with dependent data using deep neural networks, achieving reliable estimates without sample splitting, and paving the way for broader semiparametric applications.

Contribution

It demonstrates that DNN-based estimators in dependent data settings can attain $ oot{n}$-consistency and asymptotic normality without sample splitting, advancing econometric inference methods.

Findings

DNN estimators achieve $ oot{n}$-consistency in dependent data.

Asymptotic normality of the estimator is established.

Sample splitting can be avoided in dependent data inference.

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.