Distributed Bootstrap for Simultaneous Inference Under High Dimensionality

arXiv2102.10080MaRDI QIDQ6361086

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Publication date: 19 February 2021

Abstract: We propose a distributed bootstrap method for simultaneous inference on high-dimensional massive data that are stored and processed with many machines. The method produces an $el{l}_{i}nfty$-norm confidence region based on a communication-efficient de-biased lasso, and we propose an efficient cross-validation approach to tune the method at every iteration. We theoretically prove a lower bound on the number of communication rounds $a{u}_{min}$ that warrants the statistical accuracy and efficiency. Furthermore, $a{u}_{min}$ only increases logarithmically with the number of workers and the intrinsic dimensionality, while nearly invariant to the nominal dimensionality. We test our theory by extensive simulation studies, and a variable screening task on a semi-synthetic dataset based on the US Airline On-Time Performance dataset. The code to reproduce the numerical results is available at GitHub: https://github.com/skchao74/Distributed-bootstrap.

Has companion code repository: https://github.com/skchao74/Distributed-bootstrap

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