Distributed Bootstrap Simultaneous Inference for High-Dimensional Quantile Regression

Xingcai Zhou, Zhaoyang Jing and Chao Huang ()
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Xingcai Zhou: School of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, China
Zhaoyang Jing: School of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, China
Chao Huang: Department of Statistics, Florida State University, Tallahassee, FL 32306, USA

Mathematics, 2024, vol. 12, issue 5, 1-53

Abstract: Modern massive data with enormous sample size and tremendous dimensionality are usually impossible to process with a single machine. They are typically stored and processed in a distributed manner. In this paper, we propose a distributed bootstrap simultaneous inference for a high-dimensional quantile regression model using massive data. Meanwhile, a communication-efficient (CE) distributed learning algorithm is developed via the CE surrogate likelihood framework and ADMM procedure, which can handle the non-smoothness of the quantile regression loss and the Lasso penalty. We theoretically prove the convergence of the algorithm and establish a lower bound on the number of communication rounds ι min that warrant statistical accuracy and efficiency. The distributed bootstrap validity and efficiency are corroborated by an extensive simulation study.

Keywords: distributed statistical learning; multiplier bootstrap; quantile regression; communication efficiency; ADMM algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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