A scalable bootstrap for massive data

The bootstrap provides a simple and powerful means of assessing the quality of esti-mators. However, in settings involving large datasets—which are increasingly prevalent— the computation of bootstrap-based quantities can be prohibitively demanding com-putationally. While variants such as subsampling and the m out of n bootstrap can be used in principle to reduce the cost of bootstrap computations, we find that these meth-ods are generally not robust to specification of hyperparameters (such as the number of subsampled data points), and they often require use of more prior information (such as rates of convergence of estimators) than the bootstrap. As an alternative, we intro-duce the Bag of Little Bootstraps (BLB), a new procedure which incorporates features of both the bootstrap and subsampling to yield a robust, computationally efficient 1 ar X i