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2020 Detection of sparse positive dependence
Ery Arias-Castro, Rong Huang, Nicolas Verzelen
Electron. J. Statist. 14(1): 702-730 (2020). DOI: 10.1214/19-EJS1675

Abstract

In a bivariate setting, we consider the problem of detecting a sparse contamination or mixture component, where the effect manifests itself as a positive dependence between the variables, which are otherwise independent in the main component. We first look at this problem in the context of a normal mixture model. In essence, the situation reduces to a univariate setting where the effect is a decrease in variance. In particular, a higher criticism test based on the pairwise differences is shown to achieve the detection boundary defined by the (oracle) likelihood ratio test. We then turn to a Gaussian copula model where the marginal distributions are unknown. Standard invariance considerations lead us to consider rank tests. In fact, a higher criticism test based on the pairwise rank differences achieves the detection boundary in the normal mixture model, although not in the very sparse regime. We do not know of any rank test that has any power in that regime.

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Ery Arias-Castro. Rong Huang. Nicolas Verzelen. "Detection of sparse positive dependence." Electron. J. Statist. 14 (1) 702 - 730, 2020. https://doi.org/10.1214/19-EJS1675

Information

Received: 1 November 2018; Published: 2020
First available in Project Euclid: 30 January 2020

zbMATH: 07163271
MathSciNet: MR4057605
Digital Object Identifier: 10.1214/19-EJS1675

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