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November 2019 Signal detection via Phi-divergences for general mixtures
Marc Ditzhaus
Bernoulli 25(4A): 3041-3068 (November 2019). DOI: 10.3150/18-BEJ1079


The family of goodness-of-fit tests based on $\Phi$-divergences is known to be optimal for detecting signals hidden in high-dimensional noise data when the heterogeneous normal mixture model is underlying. This test family includes Tukey’s popular higher criticism test and the famous Berk–Jones test. In this paper we address the open question whether the tests’ optimality is still present beyond the prime normal mixture model. On the one hand, we transfer the known optimality of the higher criticism test for different models, for example, for the heteroscedastic normal, general Gaussian and exponential-$\chi^{2}$-mixture models, to the whole test family. On the other hand, we discuss the optimality for new model classes based on exponential families including the scale exponential, the scale Fréchet and the location Gumbel models. For all these examples we apply a general machinery which might be used to show the tests’ optimality for further models/model classes in future.


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Marc Ditzhaus. "Signal detection via Phi-divergences for general mixtures." Bernoulli 25 (4A) 3041 - 3068, November 2019.


Received: 1 March 2018; Revised: 1 August 2018; Published: November 2019
First available in Project Euclid: 13 September 2019

zbMATH: 07110120
MathSciNet: MR4003573
Digital Object Identifier: 10.3150/18-BEJ1079

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability


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Vol.25 • No. 4A • November 2019
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