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Simultaneous Inference for Massive Data: Distributed Bootstrap

by   Yang Yu, et al.

In this paper, we propose a bootstrap method applied to massive data processed distributedly in a large number of machines. This new method is computationally efficient in that we bootstrap on the master machine without over-resampling, typically required by existing methods <cit.>, while provably achieving optimal statistical efficiency with minimal communication. Our method does not require repeatedly re-fitting the model but only applies multiplier bootstrap in the master machine on the gradients received from the worker machines. Simulations validate our theory.


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