This paper presents a general framework for estimating high-dimensional conditional latent factor models via constrained nuclear norm regularization. We establish large sample properties of the estimators and provide efficient algorithms for their computation. To improve practical applicability, we propose a cross-validation procedure for selecting the regularization parameter. Our framework unifies the estimation of various conditional factor models, enabling the derivation of new asymptotic results while addressing limitations of existing methods, which are often model-specific or restrictive. Empirical analyses of the cross section of individual US stock returns suggest that imposing homogeneity improves the model's out-of-sample predictability, with our new method outperforming existing alternatives.

翻译：本文提出了一种通过约束核范数正则化来估计高维条件潜在因子模型的通用框架。我们建立了估计量的大样本性质，并提供了高效的计算算法。为提高实际适用性，我们提出了一种用于选择正则化参数的交叉验证程序。我们的框架统一了各类条件因子模型的估计，在解决现有方法（通常具有模型特定性或限制性）局限性的同时，能够推导出新的渐近结果。对美国个股横截面收益的实证分析表明，施加同质性假设可提升模型的样本外预测能力，且我们提出的新方法优于现有替代方案。