Optimal distributed testing in high-dimensional Gaussian models

The rapidly increasing amount of available data in many fields of application has triggered the development of distributed methods for data analysis. Distributed methods, besides being able to speed up computations considerably, can reduce local memory requirements and can also help in protecting privacy, by refraining from storing a whole dataset in a single central location. Moreover, distributed methods occur naturally when data is by construction observed and processed at multiple locations, such as for instance in astronomy, meteorology, seismology, military radar or air traffic control systems. The information theoretic aspects of distributed statistical methods have only been studied rigorously relatively recently. Most work up till now has focussed on distributed methods for estimating a signal in the normal-means model under bandwidth, or communication restrictions (see for instance [23, 6, 4, 7]) and, related to that, on deriving minimix lower bounds and optimal distributed estimation strategies in the context of nonparametric regression, density estimation and Gaussian signal-in-white-noise models (e.g.