Abstract: Suppose that an observed countis of the form
, where the background
and the signal
are independent Poisson random variables with parameters
and
,
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
; that is, if
is observed, then the suggestion is to base the inference on the conditional distribution of
given
. This suggestion is used here to derive an estimator of the signal, and the estimator is shown to be admissible and minimax.
Key words and phrases: Admissible, Confidence and credible interval, coverage probability, mean square error, minimax, signal plus background.