## Bernoulli

• Bernoulli
• Volume 25, Number 4A (2019), 3041-3068.

### Signal detection via Phi-divergences for general mixtures

Marc Ditzhaus

#### Abstract

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.

#### Article information

Source
Bernoulli, Volume 25, Number 4A (2019), 3041-3068.

Dates
Revised: August 2018
First available in Project Euclid: 13 September 2019

https://projecteuclid.org/euclid.bj/1568362051

Digital Object Identifier
doi:10.3150/18-BEJ1079

Mathematical Reviews number (MathSciNet)
MR4003573

Zentralblatt MATH identifier
07110120

#### Citation

Ditzhaus, Marc. Signal detection via Phi-divergences for general mixtures. Bernoulli 25 (2019), no. 4A, 3041--3068. doi:10.3150/18-BEJ1079. https://projecteuclid.org/euclid.bj/1568362051

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