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Empirical tail conditional allocation and its consistency under minimal assumptions

Author

Listed:
  • N. V. Gribkova

    (Saint Petersburg State University
    Emperor Alexander I St. Petersburg State Transport University)

  • J. Su

    (Purdue University
    York University)

  • R. Zitikis

    (York University
    Western University)

Abstract

Under minimal assumptions, we prove that an empirical estimator of the tail conditional allocation (TCA), also known as the marginal expected shortfall, is consistent. Examples are provided to confirm the minimality of the assumptions. A simulation study illustrates the performance of the estimator in the context of developing confidence intervals for the TCA. The philosophy adopted in the present paper relies on three principles: easiness of practical use, mathematical rigor, and practical justifiability and verifiability of assumptions.

Suggested Citation

  • N. V. Gribkova & J. Su & R. Zitikis, 2022. "Empirical tail conditional allocation and its consistency under minimal assumptions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 713-735, August.
    • Handle: RePEc:spr:aistmt:v:74:y:2022:i:4:d:10.1007_s10463-021-00813-3
    DOI: 10.1007/s10463-021-00813-3
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    References listed on IDEAS

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    Cited by:

    1. Yunran Wei & Ricardas Zitikis, 2022. "Assessing the difference between integrated quantiles and integrated cumulative distribution functions," Papers 2210.16880, arXiv.org, revised Apr 2023.
    2. Gribkova, N.V. & Su, J. & Zitikis, R., 2022. "Inference for the tail conditional allocation: Large sample properties, insurance risk assessment, and compound sums of concomitants," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 199-222.
    3. Wei, Yunran & Zitikis, Ričardas, 2023. "Assessing the difference between integrated quantiles and integrated cumulative distribution functions," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 163-172.

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