Distributed estimation of spiked eigenvalues in spiked population models

Abstract

The proliferation of science and technology has led to the prevalence of voluminous data sets distributed across multiple machines. Conventional statistical methodologies may be infeasible in analyzing such massive data sets due to prohibitively long computing durations, memory constraints, communication overheads, and confidentiality considerations. In this paper, we propose distributed estimators of the spiked eigenvalues in spiked population models. The consistency and asymptotic normality of the distributed estimators are derived, and the statistical error analysis of the distributed estimators is also provided. Compared to the estimation from the full sample, the proposed distributed estimation shares the same order of convergence. Simulation study and real data analysis indicate that the proposed distributed estimation and testing procedures have excellent properties in terms of estimation accuracy and stability as well as transmission efficiency.