Fan et al. (Ann Stat 47(6):3009–3031, 2019) constructed a distributed principal component analysis (PCA) algorithm to reduce the communication cost between multiple servers significantly. However, their algorithm’s guarantee is only for sub-Gaussian data. Spurred by this deficiency, this paper enhances the effectiveness of their distributed PCA algorithm by utilizing robust covariance matrix estimators of Minsker (Ann Stat 46(6A):2871–2903, 2018) and Ke et al. (Stat Sci 34(3):454–471, 2019) to tame heavy-tailed data. The theoretical results demonstrate that when the sampling distribution is symmetric innovation with the bounded fourth moment or asymmetric with the finite 6th moment, the statistical error rate of the final estimator produced by the robust algorithm is similar to that of sub-Gaussian tails. Extensive numerical trials support the theoretical analysis and indicate that our algorithm is robust to heavy-tailed data and outliers.

范等人。(Ann Stat 47(6):3009–3031, 2019) 构建了分布式主成分分析 (PCA) 算法以显着降低多台服务器之间的通信成本。然而，他们的算法的保证仅适用于亚高斯数据。由于这一缺陷，本文通过利用 Minsker (Ann Stat 46(6A):2871–2903, 2018) 和 Ke 等人的稳健协方差矩阵估计器增强了其分布式 PCA 算法的有效性。（Stat Sci 34(3):454–471, 2019）驯服重尾数据。理论结果表明，当采样分布为有界四阶矩对称创新或有限六阶矩不对称时，鲁棒算法产生的最终估计量的统计误差率与亚高斯尾的统计误差率相似。