Scalable subsampling: computation, aggregation and inference

Subsampling is a general statistical method developed in the 1990s aimed at estimating the sampling distribution of a statistic θ̂n in order to conduct nonparametric inference such as the construction of confidence intervals and hypothesis tests. Subsampling has seen a resurgence in the Big Data era where the standard, full-resample size bootstrap can be infeasible to compute. Nevertheless, even choosing a single random subsample of size b can be computationally challenging with both b and the sample size n being very large. In the paper at hand, we show how a set of appropriately chosen, non-random subsamples can be used to conduct effective—and computationally feasible—distribution estimation via subsampling. Further, we show how the same set of subsamples can be used to yield a procedure for subsampling aggregation—also known as subagging—that is scalable with big data. Interestingly, the scalable subagging estimator can be tuned to have the same (or better) rate of convergence as compared to θ̂n. The paper is concluded by showing how to conduct inference, e.g., confidence intervals, based on the scalable subagging estimator instead of the original θ̂n.