Statistical Properties of Deep Neural Networks with Dependent Data

Chad Brown

Papers from arXiv.org

Abstract: This paper establishes statistical properties of deep neural network (DNN) estimators under dependent data. Two general results for nonparametric sieve estimators directly applicable to DNN estimators are given. The first establishes rates for convergence in probability under nonstationary data. The second provides non-asymptotic probability bounds on $\mathcal{L}^{2}$-errors under stationary $\beta$-mixing data. I apply these results to DNN estimators in both regression and classification contexts imposing only a standard H\"older smoothness assumption. The DNN architectures considered are common in applications, featuring fully connected feedforward networks with any continuous piecewise linear activation function, unbounded weights, and a width and depth that grows with sample size. The framework provided also offers potential for research into other DNN architectures and time-series applications.

Date: 2024-10, Revised 2025-01
New Economics Papers: this item is included in nep-big, nep-cmp and nep-ecm
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