This paper introduces a consistent estimator and rate of convergence for the precision matrix of asset returns in large portfolios using a non-linear factor model within the deep learning framework. Our estimator remains valid even in low signal-to-noise ratio environments typical for financial markets and is compatible with weak factors. Our theoretical analysis establishes uniform bounds on expected estimation risk based on deep neural networks for an expanding number of assets. Additionally, we provide a new consistent data-dependent estimator of error covariance in deep neural networks. Our models demonstrate superior accuracy in extensive simulations and the empirics.

翻译：本文提出了一种在深度学习框架内，利用非线性因子模型对大投资组合中资产收益率的精度矩阵进行一致估计的方法，并给出了收敛速率。即使在金融市场典型的低信噪比环境下，我们的估计量仍然有效，并且与弱因子兼容。我们的理论分析基于深度神经网络，为资产数量不断扩大的情况建立了预期估计风险的统一上界。此外，我们提出了一种新的、依赖于数据的一致性误差协方差估计量，用于深度神经网络。在广泛的模拟和实证研究中，我们的模型展现了优越的准确性。