Statistica Sinica 15(2005), 59-72

ADMISSIBLE MINIMAX ESTIMATION OF THE SIGNAL

WITH KNOWN BACKGROUND

Tonglin Zhang and Michael Woodroofe

Purdue University and The University of Michigan

Abstract: 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 $\theta$, $b$ is known, but $\theta$ 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 $B\le n$. 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.