Estimating a Signal In the Presence of an Unknown Background

We describe a method for fitting distributions to data which only requires knowledge of the parametric form of either the signal or the background but not both. The unknown distribution is fit using a non-parametric kernel density estimator. The method returns parameter estimates as well as errors on those estimates. Simulation studies show that these estimates are unbiased and that the errors are correct

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. Such a bias is commonly present when a "minimization" and an "evaluation" are done at the same time. We propose to use a variant of the bootstrap to adjust the limits. A Monte Carlo study shows that these new limits have correct coverage.Comment: 14 pages, 5 figue

Limits and Confidence Intervals in the Presence of Nuisance Parameters

We study the frequentist properties of confidence intervals computed by the method known to statisticians as the Profile Likelihood. It is seen that the coverage of these intervals is surprisingly good over a wide range of possible parameter values for important classes of problems, in particular whenever there are additional nuisance parameters with statistical or systematic errors. Programs are available for calculating these intervals.Comment: 6 figure