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

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  • Denuit, Michel
  • 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," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:jmvana:v:186:y:2021:i:c:s0047259x21000816
    DOI: 10.1016/j.jmva.2021.104803
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    References listed on IDEAS

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    1. Denuit, Michel & Dhaene, Jan, 2012. "Convex order and comonotonic conditional mean risk sharing," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 265-270.
    2. Vali Asimit & Liang Peng & Ruodu Wang & Alex Yu, 2019. "An efficient approach to quantile capital allocation and sensitivity analysis," Mathematical Finance, Wiley Blackwell, vol. 29(4), pages 1131-1156, October.
    3. Takaaki Koike & Mihoko Minami, 2019. "Estimation of risk contributions with MCMC," Quantitative Finance, Taylor & Francis Journals, vol. 19(9), pages 1579-1597, September.
    4. Denuit, Michel & Robert, Christian Y., 2021. "From risk sharing to pure premium for a large number of heterogeneous losses," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 116-126.
    5. Takaaki Koike & Mihoko Minami, 2017. "Estimation of Risk Contributions with MCMC," Papers 1702.03098, arXiv.org, revised Jan 2019.
    6. Denuit, Michel & Robert, Christian Y., 2021. "From risk sharing to pure premium for a large number of heterogeneous losses," LIDAM Reprints ISBA 2021001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    1. 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.
    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 & 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).
    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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