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Distribution-free tests for sparse heterogeneous mixtures

Author

Listed:
  • Ery Arias-Castro

    (University of California, San Diego)

  • Meng Wang

    (Stanford University)

Abstract

We consider the problem of detecting sparse heterogeneous mixtures from a nonparametric perspective. Specifically, we assume that the null distribution is symmetric about zero, while the true effects have positive median. We then suggest two new tests for this purpose. The main one is a form of Anderson–Darling test for symmetry and is closely related to the higher criticism. It is shown to achieve the detection boundary for the normal mixture model and, more generally, for asymptotically generalized Gaussian mixture models, in all sparsity regimes. The other test is a form of longest run test and specifically designed for the very sparse situation.

Suggested Citation

  • Ery Arias-Castro & Meng Wang, 2017. "Distribution-free tests for sparse heterogeneous mixtures," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 71-94, March.
    • Handle: RePEc:spr:testjl:v:26:y:2017:i:1:d:10.1007_s11749-016-0499-x
    DOI: 10.1007/s11749-016-0499-x
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    References listed on IDEAS

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    1. Yu I. Ingster & Alexandre B. Tsybakov & N. Verzelzn, 2010. "Detection Boundary in Sparse Regression," Working Papers 2010-28, Center for Research in Economics and Statistics.
    2. Aurore Delaigle & Peter Hall & Jiashun Jin, 2011. "Robustness and accuracy of methods for high dimensional data analysis based on Student's t‐statistic," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(3), pages 283-301, June.
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    Cited by:

    1. Zhao, Sihai Dave & Cai, T. Tony & Li, Hongzhe, 2017. "Optimal detection of weak positive latent dependence between two sequences of multiple tests," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 169-184.

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