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
Barndorff-Nielsen, O.: On a formula for the distribution of the maximum likelihood estimator. Biometrika 70, 343–365 (1983)
Brazzale, A.R., Davison, A.C., Reid, N.: Applied Asymptotics: Case Studies in Small-Sample Statistics. Cambridge University Press, Cambridge (2007)
R Core Team: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna, Austria (2013)
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)
Gini, C.: L’ammontare e la composizione della ricchezza delle nazioni. Fratelli Bocca, Torino (1914)
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)
Meyer, C.: The bivariate normal copula. Commun Stat-Theory Methods 42, 2402–2422 (2013)
Reid, N.: Asymptotics and the theory of inference. Ann Stat 31, 1695–1731 (2003)
Reid, N., Fraser, D.A.S.: Mean log-likelihood and higher-order approximations. Biometrika 97, 159–170 (2010)
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)
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)
Staicu, A.M., Reid, N.: On probability matching priors. Can J Stat 36, 613–622 (2008)
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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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DOI: https://doi.org/10.1007/978-3-030-05420-5_6
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