Asymptotic Properties of ReLU FFN Sieve Estimators

Fabozzi Frank J. (), Fallahgoul Hasan (), Franstianto Vincentius () and Loeper Grégoire ()
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Fabozzi Frank J.: Carey Business School, Johns Hopkins University, 100 International Drive, Baltimore, MD, 21202, USA
Fallahgoul Hasan: School of Mathematics and Centre for Quantitative Finance and Investment Strategies, 2541 Monash University , 9 Rainforest Walk, 3800, Melbouren, Victoria, Australia
Franstianto Vincentius: School of Mathematics and Centre for Quantitative Finance and Investment Strategies, 2541 Monash University , 9 Rainforest Walk, 3800, Melbouren, Victoria, Australia
Loeper Grégoire: School of Mathematics and Centre for Quantitative Finance and Investment Strategies, 2541 Monash University , 9 Rainforest Walk, 3800, Melbouren, Victoria, Australia

Studies in Nonlinear Dynamics & Econometrics, 2025, vol. 29, issue 6, 727-752

Abstract: Recently, machine learning algorithms have increasing become popular tools for economic and financial forecasting. While there are several machine learning algorithms for doing so, a powerful and efficient algorithm for forecasting purposes is the multi-layer, multi-node neural network with rectified linear unit (ReLU) activation function – deep neural network (DNN). Studies have demonstrated the empirical applications of DNN but have devoted less research to investigate its statistical properties which is mainly due to its severe nonlinearity and heavy parametrization. By borrowing tools from a non-parametric regression framework, sieve estimator, we first show that there exists such a sieve estimator for a DNN. We next establish three asymptotic properties of the ReLU network: consistency, sieve-based convergence rate, and asymptotic normality, and then validate our theoretical results using Monte Carlo analysis.

Keywords: deep learning; neural networks; sieve estimators; consistency (search for similar items in EconPapers)
JEL-codes: C1 C5 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1515/snde-2023-0072

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