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• W3049649194 abstract "Higher criticism (HC) is a popular method for large-scale inference problems based on identifying unusually high proportions of small $p$-values. It has been shown to enjoy a lower-order optimality property in a simple normal location mixture model which is shared by the ‘tailor-made’ parametric generalised likelihood ratio test (GLRT) for the same model; however, HC has also been shown to perform well outside this ‘narrow’ model. We develop a higher-order framework for analysing the power of these and similar procedures, which reveals the perhaps unsurprising fact that the GLRT enjoys an edge in power over HC for the normal location mixture model. We also identify a similar parametric mixture model to which HC is similarly ‘tailor-made’ and show that the situation is (at least partly) reversed there. We also show that in the normal location mixture model a procedure based on the empirical moment-generating function enjoys the same local power properties as the GLRT and may be recommended as an easy to implement (and interpret), complementary procedure to HC. Some other practical advice regarding the implementation of these procedures is provided. Finally, we provide some simulation results to help interpret our theoretical findings." @default.
• W3049649194 created "2020-08-21" @default.
• W3049649194 creator A5013999825 @default.
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• W3049649194 date "2020-08-01" @default.
• W3049649194 modified "2023-09-25" @default.
• W3049649194 title "Beyond HC: More sensitive tests for rare/weak alternatives" @default.
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• W3049649194 doi "https://doi.org/10.1214/19-aos1885" @default.
• W3049649194 hasPublicationYear "2020" @default.
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