Testing and estimation in a sparse normal means model, with connections to shape restricted inference
author:
Jon Wellner,
Department of Statistics, University of Washington
Description
Donoho and Jin (2004), following work of Ingster (1999), studied the problem of testing
for any 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 s
∈ [−1, 2] which all achieve the Donoho-Jin-
Ingster detection boundary. I will also review recent work on estimating the proportion of non-zero
means and make some connections to shape-constrained estimation.
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