Statistical Properties of Deep Neural Networks with Dependent Data

Chad Brown

Papers from arXiv.org

Abstract: This paper develops theory for deep neural network (DNN) estimators under dependent data. To provide theory applicable to a variety of DNN-based estimators, I first establish nonasymptotic probability bounds on the theoretical and empirical $\mathcal{L}^{2}$-errors of nonparametric sieve estimators for a general class of estimation problems under possibly nonstationary $\beta$-mixing data taking values in unbounded sets. I then apply the theory to fully connected and convolutional DNN estimators without bounds or sparsity restrictions on the DNN weights. For both DNN classes, I derive general results when the function to be estimated is H\"older smooth and the data are nonstationary, subgaussian, and $\beta$-mixing with either exponential or polynomial decay. I then specialize these to nonparametric regression, logistic regression, and quantile regression settings. Under exponential $\beta$-mixing, the resulting estimators attain the nonparametric minimax rate of Stone (1982) up to logarithmic factors.

Date: 2024-10, Revised 2026-09
New Economics Papers: this item is included in nep-big, nep-cmp and nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://arxiv.org/pdf/2410.11113 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2410.11113

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().