  The bootstrap is a popular and powerful method for assessing precision of
estimators and inferential methods. However, for massive datasets which are
increasingly prevalent, the bootstrap becomes prohibitively costly in
computation and its feasibility is questionable even with modern parallel
computing platforms. Recently Kleiner, Talwalkar, Sarkar, and Jordan (2014)
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.
