Accounting for uncertainty in Data quality is important for accurate statistical inference. We aim to an optimal conservative allocation for a large universe of assets in mean-variance portfolio (MVP), which is the worst choice within uncertainty in data distribution. Unlike the low dimensional MVP studied in Blanchet et al. (2022, Management Science), the large number of assets raises a challenging problem in quantifying the uncertainty, due to the big deviation of the sample covariance matrix from the population version. To overcome this difficulty, we propose a data-adaptive method to quantify the uncertainty with the help of a factor structure. Monte-Carlo Simulation is conducted to show the superiority of our method in high-dimensional cases, that, avoiding the over-conservative results in Blanchet et al. (2022), our allocation is closer to the oracle version in terms of risk minimization and expected portfolio return controlling.

翻译：在统计推断中，考虑数据质量的不确定性对于获得准确结果至关重要。本文旨在为均值-方差投资组合（MVP）中的大规模资产集合寻求一种最优的保守配置，该配置是在数据分布不确定性范围内的最坏情况选择。与Blanchet等人（2022, Management Science）研究的低维MVP不同，资产数量庞大导致样本协方差矩阵与总体协方差矩阵存在显著偏差，这为量化不确定性带来了挑战。为克服这一困难，我们提出一种数据自适应方法，借助因子结构来量化不确定性。通过蒙特卡洛模拟验证了所提方法在高维情况下的优越性：相较于Blanchet等人（2022）方法中可能出现的过度保守结果，我们的配置在风险最小化和预期投资组合收益控制方面更接近理论最优版本。