On thresholds for robust goodness-of-fit tests

Goodness-of-fit tests are statistical procedures used to test the hypothesis H₀ that a set of observations were drawn according to some given probability distribution. Decision thresholds used in goodness-of-fit tests are typically set for guaranteeing a target false-alarm probability. In many popular testing procedures results on the weak convergence of the test statistics are used for setting approximate thresholds when exact computation is infeasible. In this work, we study robust procedures for goodness-of-fit where accurate models are not available for the distribution of the observations under hypothesis H₀. We develop procedures for setting thresholds in two specific examples - a robust version of the Kolmogorov-Smirnov test for continuous alphabets and a robust version of the Hoeffding test for finite alphabets.