Correcting the minimization bias in searches for small signals

We discuss a method for correcting the bias in the limits for small signals if those limits were found based on cuts that were chosen by minimizing a criterion such as sensitivity. This type of bias is commonly present when a “minimization” and an “evaluation” are done at the same time. We propose to use a variant of the statistical bootstrap to adjust the limits. A Monte Carlo study shows that these new limits have correct coverage.