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Original Articles

Extending the inference function for augmented margins method to implement trivariate Clayton copula-based SUR Tobit models

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Pages 1375-1401 | Received 18 Jan 2018, Accepted 13 Dec 2018, Published online: 23 Jan 2019

References

  • Abegaz, F., and E. Wit. 2015. Copula Gaussian graphical models with penalized ascent Monte Carlo EM algorithm. Statistica Neerlandica 69 (4):419–41. doi: 10.1111/stan.12066.
  • Akaike, H. 1977. On entropy maximization principle. In Applications of statistics, ed. P. R. Krishnaiah, 27–41. North-Holland: Amsterdam.
  • Anastasopoulos, P. C., V. N. Shankar, J. E. Haddock, and F. L. Mannering. 2012. A multivariate Tobit analysis of highway accident-injury-severity rates. Accident Analysis & Prevention 45:110–9. doi: 10.1016/j.aap.2011.11.006.
  • Baranchuk, N., and S. Chib. 2008. Assessing the role of option grants to CEOs: How important is heterogeneity? Journal of Empirical Finance 15 (2):145–66. doi: 10.1016/j.jempfin.2006.10.004.
  • Brown, E., and H. Lankford. 1992. Gifts of money and gifts of time: estimating the effects of tax prices and available time. Journal of Public Economics 47 (3):321–41. doi: 10.1016/0047-2727(92)90032-B.
  • Chen, S., and X. Zhou. 2011. Semiparametric estimation of a bivariate Tobit model. Journal of Econometrics 165 (2):266–74. doi: 10.1016/j.jeconom.2011.07.005.
  • Cherubini, U., E. Luciano, and W. Vecchiato. 2004. Copula methods in finance. Chichester: John Wiley & Sons.
  • Chib, S. 1992. Bayes inference in the Tobit censored regression model. Journal of Econometrics 51 (1-2):79–99. doi: 10.1016/0304-4076(92)90030-U.
  • Chib, S., and E. Greenberg. 1998. Analysis of multivariate probit models. Biometrika 85 (2):347–61. doi: 10.1093/biomet/85.2.347.
  • Clayton, D. G. 1978. A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65 (1):141–52. doi: 10.2307/2335289.
  • Davison, A. C., and D. V. Hinkley. 1997. Bootstrap methods and their application. Cambridge: Cambridge University Press.
  • De Luca, G., and G. Rivieccio. 2012. Multivariate tail dependence coefficients for Archimedean copulae. In Advanced statistical methods for the analysis of large Data-Sets, eds. A. Di Ciaccio, M. Coli, and J. M. Angulo Ibañez, 287–296. Berlin: Springer.
  • Devroye, L. 1986. Non-uniform random variate generation. New York: Springer-Verlag.
  • Di Bernardino, E., and D. Rullière. 2014. On tail dependence coefficients of transformed multivariate Archimedean copulas. Unpublished paper available at: https://hal.archives-ouvertes.fr/hal-00992707v2/document.
  • Efron, B., and R. J. Tibshirani. 1993. An introduction to the bootstrap. New York: Chapman & Hall.
  • Ferreira, P. H., and F. Louzada. 2017. Maximum likelihood estimation for bivariate SUR Tobit modeling in presence of two right-censored dependent variables. Communications in Statistics—Simulation and Computation (Online), 1–19. doi: 10.1080/03610918.2017.1375521.
  • Genest, C., J. Nešlehová, and N. Ben Ghorbal. 2011. Estimators based on Kendall’s tau in multivariate copula models. Australian & New Zealand Journal of Statistics 53:157–77. doi: 10.1111/j.1467-842X.2011.00622.x.
  • Genest, C., B. Remillard, and D. Beaudoin. 2009. Goodness-of-fit tests for copulas: A review and a power study. Insurance: Mathematics and Economics 44:199–213. doi: 10.1016/j.insmatheco.2007.10.005.
  • Geweke, J. 1991. Efficient simulation from the multivariate normal and Student-t distributions subject to linear constraints and the evaluation of constraint probabilities. Computing science and statistics: Proceedings of the 23rd symposium on the interface, 571–578, Seattle, USA.
  • Greene, W. H. 2003. Econometric analysis. New Jersey: Prentice Hall.
  • Gribkova, S., and O. Lopez. 2015. Non-parametric copula estimation under bivariate censoring. Scandinavian Journal of Statistics 42 (4):925–46. doi: 10.1111/sjos.12144.
  • Hinkley, D. V. 1988. Bootstrap methods. Journal of the Royal Statistical Society Series B 50:321–37. doi: 10.1111/j.2517-6161.1988.tb01731.x.
  • Huang, C. J., F. A. Sloan, and K. W. Adamache. 1987. Estimation of seemingly unrelated Tobit regressions via the EM algorithm. Journal of Business and Economic Statistics 5:425–30. doi: 10.2307/1391618.
  • Huang, H. C. 1999. Estimation of the SUR Tobit model via the MCECM algorithm. Economic Letters 64 (1):25–30. doi: 10.1016/S0165-1765(99)00075-0.
  • Huang, H. C. 2001. Bayesian analysis of the SUR Tobit model. Applied Economics Letters 8 (9):617–22. doi: 10.1080/13504850010026069.
  • Joe, H. 2014. Dependence modeling with copulas. London: Chapman & Hall.
  • Joe, H., and J. J. Xu. 1996. The estimation method of inference functions for margins for multivariate models. Technical report 166. Department of Statistics, University of British Columbia.
  • Kamakura, W. A., and M. Wedel. 2001. Exploratory Tobit factor analysis for multivariate censored data. Multivariate Behavioral Research 36 (1):53–82. doi: 10.1207/S15327906MBR3601_03.
  • Lee, L. F. 1993. Multivariate Tobit models in econometrics. In Handbook of statistics, eds. G. S. Maddala, C. R. Rao, and H. D. Vinod. vol. 11, 145–173. North-Holland: Amsterdam.
  • Louzada, F., and P. H. Ferreira. 2015. On the classical estimation of bivariate copula-based seemingly unrelated Tobit models through the proposed inference function for augmented margins method. Journal of Data Science 13:771–94.
  • Louzada, F., and P. H. Ferreira. 2016. Modified inference function for margins for the bivariate clayton copula-based SUN Tobit model. Journal of Applied Statistics 43 (16):2956–76. doi: 10.1080/02664763.2016.1155204.
  • Malik, H. J., and B. Abraham. 1973. Multivariate logistic distributions. The Annals of Statistics 1 (3):588–90. doi: 10.1214/aos/1176342430.
  • Meng, X., and D. B. Rubin. 1996. Efficient methods for estimating and testing seemingly unrelated regressions in the presence of latent variables and missing observations. In Bayesian analysis in statistics and econometrics, eds. D. A. Berry, K. M. Chaloner, and J. K. Geweke, 215–227. New York: John Wiley & Sons.
  • Moulton, L. H., and N. A. Halsey. 1995. A mixture model with detection limits for regression analyses of antibody response to vaccine. Biometrics 51 (4):1570–8. doi: 10.2307/2533289.
  • Nelsen, R. B. 2006. An introduction to copulas. 2nd ed. New York: Springer.
  • Pitt, M., D. Chan, and R. Kohn. 2006. Efficient Bayesian inference for Gaussian copula regression models. Biometrika 93 (3):537–54. doi: 10.1093/biomet/93.3.537.
  • R Core Team. 2014. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. Available at: http://www.R-project-org/.
  • Schwarz, G. E. 1978. Estimating the dimension of a model. The Annals of Statistics 6 (2):461–4. doi: 10.1214/aos/1176344136.
  • Shih, J. H., and T. A. Louis. 1995. Inferences on the association parameter in copula models for bivariate survival data. Biometrics 51 (4):1384–99.
  • Sklar, A. 1959. Fonctions de répartition à n dimensions et leurs marges. Publications de L’Institut de Statistique de L’Université de Paris 8:229–31.
  • Smith, M. S., and M. A. Khaled. 2012. Estimation of copula models with discrete margins via Bayesian data augmentation. Journal of the American Statistical Association 107 (497):290–303. doi: 10.1080/01621459.2011.644501.
  • Su, L. J., and L. Arab. 2006. Salad and raw vegetable consumption and nutritional status in the adult US population: Results from the third national health and nutrition examination survey. Journal of the American Dietetic Association 106 (9):1394–404. doi: 10.1016/j.jada.2006.06.004.
  • Sun, L., L. Wang, and J. Sun. 2006. Estimation of the association for bivariate interval-censored failure time data. Scandinavian Journal of Statistics 33 (4):637–49. doi: 10.1111/j.1467-9469.2006.00502.x.
  • Sungur, E. A. 1999. Truncation invariant dependence structures. Communications in Statistics—Theory and Methods 28 (11):2553–68. doi: 10.1080/03610929908832438.
  • Sungur, E. A. 2002. Some results on truncation dependence invariant class of copulas. Communications in Statistics—Theory and Methods 31 (8):1399–422. doi: 10.1081/STA-120006076.
  • Taylor, M. R., and D. Phaneuf. 2009. Bayesian estimation of the impacts of food safety information on household demand for meat and poultry. In: Proceedings of the 2009 AAEA & ACCI Joint Annual Meeting, p. 26–28, Milwaukee, USA.
  • Tobin, J. 1958. Estimation of relationships for limited dependent variables. Econometrica 26 (1):24–36. doi: 10.2307/1907382.
  • Trivedi, P. K., and D. M. Zimmer. 2006. Copula modeling: An introduction for practitioners. Foundations and Trends® in Econometrics 1 (1):1–111. doi: 10.1561/0800000005.
  • USDA. 2000. Continuing survey of food intakes by individuals 1994-1996. CD-ROM. Washington, DC: Agricultural Research Service.
  • Wales, T. J., and A. D. Woodland. 1983. Estimation of consumer demand systems with binding non-negativity constraints. Journal of Econometrics 21 (3):263–85. doi: 10.1016/0304-4076(83)90046-5.
  • Wichitaksorn, N., S. T. B. Choy, and R. Gerlach. 2012. Estimation of bivariate copula-based seemingly unrelated Tobit models. Working paper, Discipline of Business Analytics, University of Sydney Business School, Australia.
  • Zellner, A. 1962. An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias. Journal of the American Statistical Association 57 (298):348–68. doi: 10.2307/2281644.
  • Zellner, A., and T. Ando. 2010. Bayesian and non-Bayesian analysis of the seemingly unrelated regression model with student-t errors, and its application for forecasting. International Journal of Forecasting 26 (2):413–34.

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