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Integrated depth for measurable functions and sets

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  • Nagy, Stanislav

Abstract

Measurability, and uniform strong consistency of the integrated depths for functional data are established for the case when the random functions are Borel measurable. First consistent depths applicable to set-valued, and fuzzy data are obtained.

Suggested Citation

  • Nagy, Stanislav, 2017. "Integrated depth for measurable functions and sets," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 165-170.
    • Handle: RePEc:eee:stapro:v:123:y:2017:i:c:p:165-170
    DOI: 10.1016/j.spl.2016.12.012
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    References listed on IDEAS

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    1. Gijbels, Irène & Nagy, Stanislav, 2015. "Consistency of non-integrated depths for functional data," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 259-282.
    2. López-Pintado, Sara & Romo, Juan, 2009. "On the Concept of Depth for Functional Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 718-734.
    3. Ricardo Fraiman & Jean Meloche & Luis García-Escudero & Alfonso Gordaliza & Xuming He & Ricardo Maronna & Víctor Yohai & Simon Sheather & Joseph McKean & Christopher Small & Andrew Wood & R. Fraiman &, 1999. "Multivariate L-estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(2), pages 255-317, December.
    4. Kearney, Fearghal & Murphy, Finbarr & Cummins, Mark, 2015. "An analysis of implied volatility jump dynamics: Novel functional data representation in crude oil markets," The North American Journal of Economics and Finance, Elsevier, vol. 33(C), pages 199-216.
    5. Ricardo Fraiman & Graciela Muniz, 2001. "Trimmed means for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 419-440, December.
    6. González-Rodríguez, Gil & Colubi, Ana & Gil, María Ángeles, 2012. "Fuzzy data treated as functional data: A one-way ANOVA test approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 943-955.
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    Cited by:

    1. Antonio Elías & Stanislav Nagy, 2025. "Statistical properties of partially observed integrated functional depths," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 34(1), pages 125-150, March.
    2. Nagy, Stanislav & Ferraty, Frédéric, 2019. "Data depth for measurable noisy random functions," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 95-114.

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