Testing for sparse normal means: is there a signal?
Seminar Room 2, Newton Institute Gatehouse
Donoho and Jin (2004), following work of Ingster (1999), studied the problem of testing for a signal in a sparse normal means model and showed that there is a ``detection boundary'' above which the signal can be detected and below which no test has any power. They showed that Tukey's ``higher criticism'' statistic achieves the detection boundary. I will introduce a new family of test statistics based on phi-divergences (indexed by a real number s with values between -1 and 2)which all achieve the Donoho-Jin-Ingster detection boundary. I will also review recent work on estimating the proportion of non-zero means.