Distribution-free tests for sparse heterogeneous mixtures

• Ery Arias-Castro ^[2] ; Meng Wang ^[1]
  1. [1] Stanford University

     Stanford University

     Estados Unidos

     
  2. [2] University of California
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 26, Nº. 1, 2017, págs. 71-94
• Idioma: inglés
• DOI: 10.1007/s11749-016-0499-x
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.