Robust covariance estimation for distributed principal component analysis

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, paper enhances effectiveness of PCA utilizing robust covariance matrix estimators Minsker 46(6A):2871–2903, 2018) and Ke (Stat Sci 34(3):454–471, tame heavy-tailed The theoretical results demonstrate that when sampling distribution symmetric innovation with bounded fourth moment or asymmetric finite 6th moment, statistical error rate final estimator produced similar tails. Extensive numerical trials support indicate our data outliers.