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Testing for sparse normal means: is there a signal?

Wednesday 30th April 2008 - 11:00 to 12:00
INI Seminar Room 2

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.

Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons