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Frequentist and Bayesian Small-Sample Confidence Intervals for Gini’s Gamma Index in a Gaussian Bivariate Copula

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Abstract

In this paper we consider frequentist and Bayesian likelihood-based small-sample procedures to compute confidence intervals for Gini’s gamma index in the bivariate Gaussian copula model. We furthermore discuss how the method straightforwardly extends to any measure of concordance which is available in closed form, and to any type of copula for which the considered measure of concordance has a closed-form expression.

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References

  1. Barndorff-Nielsen, O.: On a formula for the distribution of the maximum likelihood estimator. Biometrika 70, 343–365 (1983)

    Article  MathSciNet  Google Scholar 

  2. Brazzale, A.R., Davison, A.C., Reid, N.: Applied Asymptotics: Case Studies in Small-Sample Statistics. Cambridge University Press, Cambridge (2007)

    Book  Google Scholar 

  3. R Core Team: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna, Austria (2013)

    Google Scholar 

  4. Fraser, D.A.S., Reid, N., Wu, J.: A simple general formula for tail probabilities for frequenstist and Bayesian inference. Biometrika 86, 249–264 (1999)

    Article  MathSciNet  Google Scholar 

  5. Gini, C.: L’ammontare e la composizione della ricchezza delle nazioni. Fratelli Bocca, Torino (1914)

    Google Scholar 

  6. Mameli, V., Brazzale, A.R.: Modern likelihood inference for the maximum/minimum of a bivariate normal vector. J Stat Comput Simul 86, 1869–1890 (2016)

    Article  MathSciNet  Google Scholar 

  7. Meyer, C.: The bivariate normal copula. Commun Stat-Theory Methods 42, 2402–2422 (2013)

    Article  MathSciNet  Google Scholar 

  8. Reid, N.: Asymptotics and the theory of inference. Ann Stat 31, 1695–1731 (2003)

    Article  MathSciNet  Google Scholar 

  9. Reid, N., Fraser, D.A.S.: Mean log-likelihood and higher-order approximations. Biometrika 97, 159–170 (2010)

    Article  MathSciNet  Google Scholar 

  10. Schmid, F., Schmidt, R., Blumentritt, T., Gaisser, S., Ruppert, M.: Copula-based measure of multivariate association. In: Jaworski, P., et al. (eds.) Copula Theory and Its Applications. Lecture Notes in Statistics, vol. 198, pp. 209–236. Springer, Berlin (2010)

    Chapter  Google Scholar 

  11. Sklar, A.: Fonctions de répartition à n dimensions et leurs marges. Publications de l’Institut de Statistique de l’Université de Paris 8, 229–231 (1959)

    MATH  Google Scholar 

  12. Staicu, A.M., Reid, N.: On probability matching priors. Can J Stat 36, 613–622 (2008)

    Article  MathSciNet  Google Scholar 

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Correspondence to Valentina Mameli .

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Mameli, V., Brazzale, A.R. (2019). Frequentist and Bayesian Small-Sample Confidence Intervals for Gini’s Gamma Index in a Gaussian Bivariate Copula. In: Crocetta, C. (eds) Theoretical and Applied Statistics. SIS 2015. Springer Proceedings in Mathematics & Statistics, vol 274. Springer, Cham. https://doi.org/10.1007/978-3-030-05420-5_6

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