Bootstrap Tilting Diagnostics

The fundamental bootstrap assumption is that the bootstrap approximates reality; that the sampling distribution of a statistic under the empirical distribution F̂ approximates the sampling distribution under the true (unknown) distribution. A natural way to test this is to investigate how the bootstrap distribution varies when F̂ is replaced by other distributions. Iterated bootstrapping, jackknife-after-bootstrap (JAB), and bootstrap tilting diagnostics all do this, but tilting lets one focus on a key questions – how the sampling distribution depends on a parameter of interest – without the noise of the other procedures. Both tilting and iterated bootstrapping may be used for calibration, and in some cases giving confidence intervals or hypothesis tests that are an order of magnitude more accurate than the uncalibrated versions. But whereas iterated bootstrapping is computationally much more expensive than ordinary bootstrapping, bootstrap tilting is less expensive – 17 to 37 times less expensive than common bootstrap confidence intervals.