%0 Journal Article
%T Distributed Estimation and Inference with Statistical Guarantees
%A Heather Battey
%A Jianqing Fan
%A Han Liu
%A Junwei Lu
%A Ziwei Zhu
%J Statistics
%D 2015
%I arXiv
%X 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.
%U http://arxiv.org/abs/1509.05457v1