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Efron’s asymptotic monotonicity property in the Gaussian stable domain of attraction

Author

Listed:
  • Denuit, Michel

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Robert, Christian Y.

Abstract

In Efron (1965), Efron studied the stochastic increasingness of the vector of independent random variables entering a sum, given the value of the sum. Precisely, he proved that log-concavity for the distributions of the random variables ensures that the vector becomes larger (in the sense of the usual multivariate stochastic order) when the sum is known to increase. This result is known as Efron’s “monotonicity property”. Under the condition that the random variables entering in the sum have density functions with bounded second derivatives, we investigate whether Efron’s monotonicity property generalizes when sums involve a large number of terms to which a central-limit theorem applies.

Suggested Citation

  • Denuit, Michel & Robert, Christian Y., 2021. "Efron’s asymptotic monotonicity property in the Gaussian stable domain of attraction," LIDAM Reprints ISBA 2021029, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2021029
    DOI: https://doi.org/10.1016/j.jmva.2021.104803
    Note: In: Journal of Multivariate Analysis, 2021, vol. 186, 104803
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    Cited by:

    1. Denuit, Michel & Dhaene, Jan & Ghossoub, Mario & Robert, Christian Y., 2023. "Comonotonicity and Pareto Optimality, with Application to Collaborative Insurance," LIDAM Discussion Papers ISBA 2023005, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Denuit, Michel & Robert, Christian Y., 2022. "Dynamic conditional mean risk sharing in the compound Poisson surplus model," LIDAM Discussion Papers ISBA 2022034, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Denuit, Michel & Robert, Christian Y., 2023. "Conditional mean risk sharing of losses at occurrence time in the compound Poisson surplus model," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 23-32.
    4. Denuit, Michel & Robert, Christian Y., 2023. "From risk reduction to risk elimination by conditional mean risk sharing of independent losses," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 46-59.
    5. Denuit, Michel & Robert, Christian Y., 2023. "Conditional mean risk sharing of independent discrete losses in large pools," LIDAM Discussion Papers ISBA 2023010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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