5601 Notes: The Subsampling Bootstrap

The term “bootstrap” was coined by Efron (1979). He described both the nonparametric and parametric bootstrap. In particular, his nonparametric bootstrap is the procedure of resampling with replacement from the original sample at the same sample size that is by far the most commonly used bootstrap procedure. It wasn’t long before people experimented with resampling at different sample sizes. But the key discovery in that area came later. Politis and Romano (1994) described resampling without replacement from the original sample at smaller than the original sample size. This is different enough from Efron’s idea that in their book (Politis, et al., 1999) they don’t call it “bootstrap” but just plain “subsampling”. Whatever you call it, here’s why it is such an important innovation.