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Distributed Estimation and Inference with Statistical Guarantees

Author(s): Battey, Heather; Fan, Jianqing; Liu, Han; Lu, Junwei; Zhu, Ziwei

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Abstract: This paper studies hypothesis testing and parameter estimation in the context of the divide and conquer algorithm. In a unified likelihood based framework, we propose new test statistics and point estimators obtained by aggregating various statistics from $k$ subsamples of size $n/k$, where $n$ is the sample size. In both low dimensional and high dimensional settings, we address the important question of how to choose $k$ as $n$ grows large, providing a theoretical upper bound on $k$ such that the information loss due to the divide and conquer algorithm is negligible. In other words, the resulting estimators have the same inferential efficiencies and estimation rates as a practically infeasible oracle with access to the full sample. Thorough numerical results are provided to back up the theory.
Publication Date: Sep-2015
Citation: Battey, Heather, Fan, Jianqing, Liu, Han, Lu, Junwei, Zhu, Ziwei. (2015). Distributed Estimation and Inference with Statistical Guarantees. arXiv:1509.05457 [math, stat]
Type of Material: Journal Article
Journal/Proceeding Title: arXiv:1509.05457 [math, stat]
Version: Author's manuscript

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