DISTRIBUTED TESTING AND ESTIMATION UNDER SPARSE HIGH DIMENSIONAL MODELS

• 成果类型: Article
• 署名作者: Battey, Heather; Fan, Jianqing; Liu, Han; Lu, Junwei; Zhu, Ziwei
• 署名单位: Imperial College London; Princeton University; Fudan University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/17-AOS1587
• 发表日期: 2018
• 页码: 1352-1382
• 关键词: nonconcave penalized likelihood; variable selection; confidence-intervals; general-theory; regression; regions

摘要

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 sparse high dimensional settings, we address the important question of how large k can be, as n grows large, such that the loss of efficiency due to the divide-and-conquer algorithm is negligible. In other words, the resulting estimators have the same inferential efficiencies and estimation rates as an oracle with access to the full sample. Thorough numerical results are provided to back up the theory.