Abstract:
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The Donoho and Jin (2004) Higher Criticism (HC) statistic is an increasingly popular tool in sparse mixture detection, feature selection, and classification problems. This talk considers the extensively studied sparse normal mixture detection problem, which has been used as a testing ground for other procedures (such as the Jager and Wellner (2007) phi-divergence statistics, of which HC is a special case).
We reveal an alternative interpretation for HC, which perhaps explains some of its strengths and weaknesses in sparse mixture detection. The implications of this reveal are established in the sparse normal mixture detection problem. In particular, we show that there are sequences of local alternatives where the generalised likelihood ratio test has limiting power one, but the Jager and Wellner (2007) procedures have no limiting power.
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