On the comparison of Shapley values for variance and standard deviation games
| العنوان: | On the comparison of Shapley values for variance and standard deviation games |
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| المؤلفون: | Giovanni Rabitti, Marcello Galeotti |
| المصدر: | Journal of Applied Probability. 58:609-620 |
| بيانات النشر: | Cambridge University Press (CUP), 2021. |
| سنة النشر: | 2021 |
| مصطلحات موضوعية: | Statistics and Probability, Computer Science::Computer Science and Game Theory, Conjecture, Covariance matrix, General Mathematics, Variance (accounting), Standard deviation, Combinatorics, Sum of normally distributed random variables, Dependent random variables, Statistics, Probability and Uncertainty, Random variable, Mathematics, Counterexample |
| الوصف: | Motivated by the problem of variance allocation for the sum of dependent random variables, Colini-Baldeschi, Scarsini and Vaccari (2018) recently introduced Shapley values for variance and standard deviation games. These Shapley values constitute a criterion satisfying nice properties useful for allocating the variance and the standard deviation of the sum of dependent random variables. However, since Shapley values are in general computationally demanding, Colini-Baldeschi, Scarsini and Vaccari also formulated a conjecture about the relation of the Shapley values of two games, which they proved for the case of two dependent random variables. In this work we prove that their conjecture holds true in the case of an arbitrary number of independent random variables but, at the same time, we provide counterexamples to the conjecture for the case of three dependent random variables. |
| تدمد: | 1475-6072 0021-9002 |
| DOI: | 10.1017/jpr.2020.106 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_________::3e6288d9dbf82ff6c07bef6d46bb3ade https://doi.org/10.1017/jpr.2020.106 |
| Rights: | CLOSED |
| رقم الانضمام: | edsair.doi...........3e6288d9dbf82ff6c07bef6d46bb3ade |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 14756072 00219002 |
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| DOI: | 10.1017/jpr.2020.106 |