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 that are distributed across multiple machines. It is an established fact that conventional statistical methodologies may be unfeasible in the analysis of 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 provided as well. 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.