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An adaptive decorrelation procedure for signal detection

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  • Hébert, Florian
  • Causeur, David
  • Emily, Mathieu

Abstract

In global testing, where a large number of pointwise test statistics are aggregated to simultaneously test for a collection of null hypotheses, the handling of dependence is a crucial issue. In various fields, more particularly in genetic epidemiology and functional data analysis, many testing methods for detecting an association signal between a response and explanatory variables have been proposed. Some aggregation procedures ignore dependence across pointwise test statistics whereas others introduce a model for decorrelation, with unclear conclusions on their relative performance. Indeed, the benefit that can be expected from decorrelation highly depends on the interplay between the structure of dependence across pointwise test statistics and the pattern of the association signal. Within a large class of test statistics covering a continuum of decorrelation approaches, an optimal procedure is introduced. This procedure is based on the maximization of an ad-hoc cumulant generating function-based distance between the null and nonnull distributions of a global test statistic, in order to adapt the aggregation of the pointwise statistics to the pattern of the association signal. A comparative study including simulations and applications to genetic association studies demonstrates that the ability of this test to detect a signal is more robust to the dependence structure than existing methods.

Suggested Citation

  • Hébert, Florian & Causeur, David & Emily, Mathieu, 2021. "An adaptive decorrelation procedure for signal detection," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    • Handle: RePEc:eee:csdana:v:153:y:2021:i:c:s0167947320301730
    DOI: 10.1016/j.csda.2020.107082
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    References listed on IDEAS

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    1. Jin-Ting Zhang & Xuehua Liang, 2014. "One-Way anova for Functional Data via Globalizing the Pointwise F-test," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 51-71, March.
    2. Ian Barnett & Rajarshi Mukherjee & Xihong Lin, 2017. "The Generalized Higher Criticism for Testing SNP-Set Effects in Genetic Association Studies," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 64-76, January.
    3. Sihai Dave Zhao & T. Tony Cai & Thomas P. Cappola & Kenneth B. Margulies & Hongzhe Li, 2017. "Sparse Simultaneous Signal Detection for Identifying Genetically Controlled Disease Genes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1032-1046, July.
    4. T. Tony Cai & Weidong Liu & Yin Xia, 2014. "Two-sample test of high dimensional means under dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(2), pages 349-372, March.
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