  In this paper we address the problem of performing statistical inference for
large scale data sets i.e., Big Data. The volume and dimensionality of the data
may be so high that it cannot be processed or stored in a single computing
node. We propose a scalable, statistically robust and computationally efficient
bootstrap method, compatible with distributed processing and storage systems.
Bootstrap resamples are constructed with smaller number of distinct data points
on multiple disjoint subsets of data, similarly to the bag of little bootstrap
method (BLB) [1]. Then significant savings in computation is achieved by
avoiding the re-computation of the estimator for each bootstrap sample.
Instead, a computationally efficient fixed-point estimation equation is
analytically solved via a smart approximation following the Fast and Robust
Bootstrap method (FRB) [2]. Our proposed bootstrap method facilitates the use
of highly robust statistical methods in analyzing large scale data sets. The
favorable statistical properties of the method are established analytically.
Numerical examples demonstrate scalability, low complexity and robust
statistical performance of the method in analyzing large data sets.
