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The zonoid region parameter depth

Author

Listed:
  • Ignacio Cascos

    (Universidad Carlos III de Madrid)

  • Giuseppe Pandolfo

    (University of Naples Federico II)

  • Beatriz Sinova

    (University of Oviedo)

Abstract

A new concept of depth for central regions is introduced. The proposed depth notion assesses how well an interval fits a given univariate distribution as its zonoid region of level 1/2, and it is extended to the multivariate setting by means of a projection argument. Since central regions capture information about location, scatter, and dependency among several variables, the new depth evaluated on an empirical zonoid region quantifies the degree of similarity (in terms of the features captured by central regions) of the corresponding sample with respect to some reference distribution. Applications to statistical process control and the joint monitoring of multivariate and interval-valued data in terms of location and scale are presented.

Suggested Citation

  • Ignacio Cascos & Giuseppe Pandolfo & Beatriz Sinova, 2023. "The zonoid region parameter depth," Statistical Papers, Springer, vol. 64(6), pages 2183-2205, December.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:6:d:10.1007_s00362-022-01380-2
    DOI: 10.1007/s00362-022-01380-2
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    References listed on IDEAS

    as
    1. Ivan Mizera & Christine H. Muller, 2004. "Location-Scale Depth," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 949-966, December.
    2. Cascos, Ignacio & López-Díaz, Miguel, 2016. "On the uniform consistency of the zonoid depth," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 394-397.
    3. Cascos, Ignacio & López-Díaz, Miguel, 2012. "Trimmed regions induced by parameters of a probability," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 306-318.
    Full references (including those not matched with items on IDEAS)

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