A Subsampled Double Bootstrap for Massive Data

• 成果类型: Article
• 署名作者: Sengupta, Srijan; Volgushev, Stanislav; Shao, Xiaofeng
• 署名单位: Virginia Polytechnic Institute & State University; University of Toronto; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2015.1080709
• 发表日期: 2016
• 页码: 1222-1232
• 关键词: functional observations; Empirical Processes; time-series; statistics; tests

摘要

The bootstrap is a popular and powerful method for assessing precision of estimators and inferential methods. However, for massive datasets that are increasingly prevalent, the bootstrap becomes prohibitively costly in computation and its feasibility is questionable even with modern parallel computing platforms. Recently, Kleiner and co-authors, proposed a method called BLB (bag of little bootstraps) for massive data, which is more computationally scalable with little sacrifice of statistical accuracy. Building on BLB and the idea of fast double bootstrap, we propose a new resampling method, the subsampled double bootstrap, for both independent data and time series data. We establish consistency of the subsampled double bootstrap under mild conditions for both independent and dependent cases. Methodologically, the subsampled double bootstrap is superior to BLB in terms of running time, more sample coverage, and automatic implementation with less tuning parameters for a given time budget. Its advantage relative to BLB and bootstrap is also demonstrated in numerical simulations and a data illustration. Supplementary materials for this article are available online.