We consider the estimation of factor model-based variance-covariance matrix when the factor loading matrix is assumed sparse. To do so, we rely on a system of penalized estimating functions to account for the identification issue of the factor loading matrix while fostering sparsity in potentially all its entries. We prove the oracle property of the penalized estimator for the factor model when the dimension is fixed. That is, the penalization procedure can recover the true sparse support, and the estimator is asymptotically normally distributed. Consistency and recovery of the true zero entries are established when the number of parameters is diverging. These theoretical results are supported by simulation experiments, and the relevance of the proposed method is illustrated by an application to portfolio allocation.

翻译：我们考虑当因子载荷矩阵被假设为稀疏时，基于因子模型的方差-协方差矩阵估计问题。为此，我们依赖一个惩罚估计方程系统，以解决因子载荷矩阵的识别问题，同时促进其所有潜在条目中的稀疏性。当维度固定时，我们证明了因子模型惩罚估计量的Oracle性质。即，该惩罚过程能够恢复真实的稀疏支撑集，且估计量渐近服从正态分布。当参数数量发散时，我们建立了估计的一致性与真实零条目的恢复性质。这些理论结果通过模拟实验得到验证，并通过投资组合分配的应用实例展示了所提方法的相关性。