Mode testing, critical bandwidth and excess mass

• Jose Ameijeiras-Alonso ^[1] ; Rosa M. Crujeiras ^[1] ; Alberto Rodríguez-Casal ^[1]
  1. [1] Universidade de Santiago de Compostela

     Universidade de Santiago de Compostela

     Santiago de Compostela, España

     
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 28, Nº. 3, 2019, págs. 900-919
• Idioma: inglés
• DOI: 10.1007/s11749-018-0611-5
• Texto completo no disponible (Saber más ...)
• Resumen

  • The identification of peaks or maxima in probability densities, by mode testing or bump hunting, has become an important problem in applied fields. For real random variables, this task has been approached in the statistical literature from different perspectives, with the proposal of testing procedures which are based on kernel density estimators or on the quantification of excess mass. However, none of the existing proposals for testing the number of modes provides a satisfactory performance in practice. In this work, a new procedure which combines the previous approaches (smoothing and excess mass) is presented together with a revision on the previous proposals. The new method is compared with the existing ones in an extensive simulation study, showing a superior behaviour, with good calibration and power results. Theoretical justification for its performance is also obtained. A real data example on philatelic data is also included for illustration purposes, revising previous approaches and discussing the results with the new procedure.