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The Scientific World Journal
Volume 2014, Article ID 347043, 24 pages
http://dx.doi.org/10.1155/2014/347043
Research Article

Identification and Forecasting in Mortality Models

1Department of Economics, University of Oxford, Oxford OX1 2JD, UK
2Programme on Economic Modelling, INET, University of Oxford, Oxford OX1 2JD, UK
3Nuffield College, Oxford OX1 1NF, UK
4Cass Business School, City University London, 106 Bunhill Row, London EC1Y 8TZ, UK

Received 22 January 2014; Accepted 17 April 2014; Published 2 June 2014

Academic Editor: Montserrat Guillén

Copyright © 2014 Bent Nielsen and Jens P. Nielsen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Ornelas, M. Guillén, and M. Alcañiz, “Implications of unisex assumptions in the analysis of longevity for insurance portfolios,” in Modeling and Simulation in Engineering, Economics, and Management, vol. 145 of Lecture Notes in Business Information Processing, pp. 99–107, 2011. View at Publisher · View at Google Scholar
  2. S. F. Jarner and E. M. Kryger, “Modelling adult mortality in small populations: the SAINT model,” ASTIN Bulletin, vol. 41, no. 2, pp. 377–418, 2011. View at Publisher · View at Google Scholar · View at Scopus
  3. R. D. Lee and L. R. Carter, “Modeling and forecasting U.S. mortality,” Journal of the American Statistical Association, vol. 87, pp. 659–671, 1992. View at Google Scholar
  4. Y. Yang, W. J. Fu, and K. C. Land, “A methodological comparison of age-period-cohort models: the intrinsic estimator and conventional generalized linear models,” Sociological Methodology, vol. 34, pp. 75–110, 2004. View at Google Scholar · View at Scopus
  5. Y. Yang and K. C. Land, “Age-period-cohort analysis of repeated cross-section surveys: fixed or random effects?” Sociological Methods & Research, vol. 36, no. 3, pp. 297–326, 2008. View at Publisher · View at Google Scholar · View at Scopus
  6. C. Berzuini and D. Clayton, “Bayesian analysis of survival on multiple time scales,” Statistics in Medicine, vol. 13, no. 8, pp. 823–838, 1994. View at Google Scholar · View at Scopus
  7. A. Riebler and L. Held, “The analysis of heterogeneous time trends in multivariate age-period-cohort models,” Biostatistics, vol. 11, no. 1, pp. 57–69, 2010. View at Publisher · View at Google Scholar · View at Scopus
  8. F. Girosi and G. King, Demographic Forecasting, Princeton University Press, Princeton, NJ, USA, 2008.
  9. E. Pitacco, M. Denuit, S. Haberman, and A. Olivieri, Modelling Longevity Dynamics for Pensions and Annuity Business, Oxford University Press, Oxford, UK, 2009.
  10. D. Kuang, B. Nielsen, and J. P. Nielsen, “Forecasting in an extended chain-ladder-type model,” Journal of Risk and Insurance, vol. 78, no. 2, pp. 345–359, 2011. View at Publisher · View at Google Scholar · View at Scopus
  11. E. Coelho and L. C. Nunes, “Forecasting mortality in the event of a structural change,” Journal of the Royal Statistical Society A: Statistics in Society, vol. 174, no. 3, pp. 713–736, 2011. View at Publisher · View at Google Scholar · View at Scopus
  12. D. R. Cox and D. V. Hinkley, Theoretical Statistics, Chapman & Hall, London, UK, 1974.
  13. O. Barndorff-Nielsen, Information and Exponential Families, John Wiley & Sons, Chichester, UK, 1978.
  14. S. R. Searle, Matrix Algebra Useful for Statistics, John Wiley & Sons, New York, NY, USA, 1982.
  15. B. Nielsen, “Power of tests for unit roots in the presence of a linear trend,” Oxford Bulletin of Economics and Statistics, vol. 70, no. 5, pp. 619–644, 2008. View at Publisher · View at Google Scholar · View at Scopus
  16. D. J. Poirier, “Revising beliefs in nonidentified models,” Econometric Theory, vol. 14, no. 4, pp. 483–509, 1998. View at Google Scholar · View at Scopus
  17. A. F. M. Smith, “Bayes estimates in one way and two way models,” Biometrika, vol. 60, no. 2, pp. 319–329, 1973. View at Google Scholar · View at Scopus
  18. J. M. Bernardo and A. F. M. Smith, Bayesian Theory, John Wiley & Sons, Chichester, UK, 2000.
  19. D. Kuang, B. Nielsen, and J. P. Nielsen, “Identification of the age-period-cohort model and the extended chain-ladder model,” Biometrika, vol. 95, no. 4, pp. 979–986, 2008. View at Publisher · View at Google Scholar · View at Scopus
  20. N. Keiding, “Statistical inference in the Lexis diagram,” Philosophical Transactions of the Royal Society of London A, vol. 332, no. 1627, pp. 487–509, 1990. View at Publisher · View at Google Scholar
  21. S. E. Fienberg and W. M. Mason, “Identification and estimation of age-period-cohort models in the analysis of discrete archival data,” Sociological Methodology, vol. 10, pp. 1–67, 1979. View at Google Scholar
  22. D. Clayton and E. Schifflers, “Models for temporal variation in cancer rates. II: age-period-cohort models,” Statistics in Medicine, vol. 6, no. 4, pp. 469–481, 1987. View at Google Scholar · View at Scopus
  23. R Development Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, 2013.
  24. M. D.M. Miranda, B. Nielsen, and J. P. Nielsen, “Inference and forecasting in the age-period-cohort model with unknown exposure with an application to mesothelioma mortality,” Journal of the Royal Statistical Society A, 2014. View at Publisher · View at Google Scholar
  25. D. Kuang, B. Nielsen, and J. P. Nielsen, “Forecasting with the age-period-cohort model and the extended chain-ladder model,” Biometrika, vol. 95, no. 4, pp. 987–991, 2008. View at Publisher · View at Google Scholar · View at Scopus
  26. P. D. England and R. J. Verrall, “Stochastic claims reserving in general insurance,” British Actuarial Journal, vol. 8, pp. 519–544, 2002. View at Google Scholar
  27. B. Zehnwirth, “Probabilistic development factor models with applications to loss reserve variability, prediction intervals, and risk based capital,” in Proceedings of the Casualty Actuarial Society Forum, pp. 447–605, Arlington, Va, USA, 1994.
  28. D. Kuang, B. Nielsen, and J. P. Nielsen, “Chain-ladder as maximum likelihood revisited,” Annals of Actuarial Science, vol. 4, pp. 105–121, 2009. View at Publisher · View at Google Scholar
  29. B. Carstensen, “Age-period-cohort models for the Lexis diagram,” Statistics in Medicine, vol. 26, no. 15, pp. 3018–3045, 2007. View at Publisher · View at Google Scholar · View at Scopus
  30. D. Clayton and E. Schifflers, “Models for temporal variation in cancer rates. I: age-period and age-cohort models,” Statistics in Medicine, vol. 6, no. 4, pp. 449–467, 1987. View at Google Scholar · View at Scopus
  31. R. M. O'Brien, “Constrained estimators and age-period-cohort models,” Sociological Methods & Research, vol. 40, no. 3, pp. 419–452, 2011. View at Publisher · View at Google Scholar · View at Scopus
  32. R. M. O'Brien, “Intrinsic estimators as constrained estimators in age-period-cohort accounting models,” Sociological Methods & Research, vol. 40, no. 3, pp. 467–470, 2011. View at Publisher · View at Google Scholar · View at Scopus
  33. W. J. Fu, K. C. Land, and Y. Yang, “On the intrinsic estimator and constrained estimators in age-period-cohort models,” Sociological Methods & Research, vol. 40, no. 3, pp. 453–466, 2011. View at Publisher · View at Google Scholar · View at Scopus
  34. L. L. Kupper, J. M. Janis, A. Karmous, and B. G. Greenberg, “Statistical age-period-cohort analysis: a review and critique,” Journal of Chronic Diseases, vol. 38, no. 10, pp. 811–830, 1985. View at Google Scholar · View at Scopus
  35. T. R. Holford, “An alternative approach to statistical age-period-cohort analysis,” Journal of Chronic Diseases, vol. 38, no. 10, pp. 831–836, 1985. View at Google Scholar · View at Scopus
  36. A. J. G. Cairns, D. Blake, K. Dowd, G. D. Coughlan, and M. Khalaf-Allah, “Bayesian stochastic mortality modeling for two populations,” ASTIN Bulletin, vol. 41, no. 1, pp. 29–59, 2011. View at Publisher · View at Google Scholar · View at Scopus
  37. S. Johansen, Likelihood-Based Inference in Cointegrated Vector Autoregressive Models, Oxford University Press, Oxford, UK, 1995.
  38. B. Nielsen, “The likelihood-ratio test for rank in bivariate canonical correlation analysis,” Biometrika, vol. 86, no. 2, pp. 279–288, 1999. View at Google Scholar · View at Scopus
  39. B. Nielsen, “Conditional test for rank in bivariate canonical correlation analysis,” Biometrika, vol. 88, no. 3, pp. 874–880, 2001. View at Google Scholar · View at Scopus
  40. A. E. Renshaw and S. Haberman, “A cohort-based extension to the Lee-Carter model for mortality reduction factors,” Insurance: Mathematics and Economics, vol. 38, no. 3, pp. 556–570, 2006. View at Publisher · View at Google Scholar · View at Scopus
  41. A. J. G. Cairns, B. David, K. Dowd et al., “A quantitative comparison of stochastic mortality models using data from England and wales and the United States,” North American Actuarial Journal, vol. 13, no. 1, pp. 1–35, 2009. View at Google Scholar · View at Scopus
  42. C. Pedroza, “A Bayesian forecasting model: predicting U.S. male mortality,” Biostatistics, vol. 7, no. 4, pp. 530–550, 2006. View at Publisher · View at Google Scholar · View at Scopus
  43. R. F. Engle and C. W. Granger, “Co-integration and error correction: representation, estimation, and testing,” Econometrica, vol. 55, pp. 251–276, 1987. View at Publisher · View at Google Scholar
  44. D. F. Hendry and B. Nielsen, Econometric Modeling, Princeton University Press, Princeton, NJ, USA, 2007.
  45. M. A. S. Cabrera, S. M. de Andrade, and R. M. Dip, “Lipids and all-cause mortality among older adults: a 12-year follow-up study,” TheScientificWorldJOURNAL, vol. 2012, Article ID 930139, 5 pages, 2012. View at Publisher · View at Google Scholar
  46. G. H. Golub and C. F. van Loan, Matrix Computations, Johns Hopkins University Press, Baltimore, Md, USA, 1989.