ADMISSIBLE MINIMAX ESTIMATION OF THE SIGNAL WITH KNOWN BACKGROUND
Tonglin Zhang, Michael B. Woodroofe · 2005
Suppose that an observed count X is of the form X = B + S, where the background B and the signal S are independent Poisson random variables with parameters b and , b is known, but is not. The model arises in astronomy and high-energy physics, and some recent articles have suggested conditioning on the observed bound for B; that is, if X = n is observed, then the suggestion is to base the inference on the conditional distribution of X given B n. This suggestion is used here to derive an estimator of the signal, and the estimator is shown to be admissible and minimax.