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Mode testing, critical bandwidth and excess mass

Author

Listed:
  • Jose Ameijeiras-Alonso

    (Universidade de Santiago de Compostela)

  • Rosa M. Crujeiras

    (Universidade de Santiago de Compostela)

  • Alberto Rodríguez-Casal

    (Universidade de Santiago de Compostela)

Abstract

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.

Suggested Citation

  • Jose Ameijeiras-Alonso & Rosa M. Crujeiras & Alberto Rodríguez-Casal, 2019. "Mode testing, critical bandwidth and excess mass," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 900-919, September.
    • Handle: RePEc:spr:testjl:v:28:y:2019:i:3:d:10.1007_s11749-018-0611-5
    DOI: 10.1007/s11749-018-0611-5
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    References listed on IDEAS

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    1. Marron, J.S. & Schmitz, H.-P., 1992. "Simultaneous Density Estimation of Several Income Distributions," Econometric Theory, Cambridge University Press, vol. 8(4), pages 476-488, December.
    2. P. M. Hartigan, 1985. "Computation of the Dip Statistic to Test for Unimodality," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 34(3), pages 320-325, November.
    3. M.‐Y. Cheng & P. Hall, 1998. "Calibrating the excess mass and dip tests of modality," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(3), pages 579-589.
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    Cited by:

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