An Exact Distribution-free One-sample Test For Equivalence

摘要

There are many exact distribution-free goodness-of-fit tests, but no equivalence testing analogues. This paper fills the gap by developing an exact one-sample distribution-free equivalence test for use with continuous distributions. We consider two continuous distributions equivalent if the pointwise distances between their distribution functions never exceed some specified constant, and we test equivalence using the supremum of the pointwise distances between the empirical distribution function and the fully specified continuous distribution of interest. The resulting test is much more powerful than a naive exact distribution-free equivalence test based on two one-sided Kolmogorov-Smirnov tests, and inversion of the test leads to distribution-free confidence bands for the unknown distribution function that are centred at the fully specified continuous distribution of interest.