Seminar Details

Seminar Details


Jan 26

3:30 pm

Testing for Sparse Normal Means: Is There a Signal?

Jon Wellner


University of Washington - Department of Statistics

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 optimal 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 briefly review recent work on estimating the proportion of non-zero means, and connect the methods to an application in astronomy/cosmology involving the Cosmic Microwave Background Radiation (CMBR).