Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-30T21:22:45.414Z Has data issue: false hasContentIssue false
  • English
  • Français

A NEW INFERENCE STRATEGY FOR GENERAL POPULATION MORTALITY TABLES

Part of: Applications Survival analysis and censored data

Published online by Cambridge University Press:  17 April 2020

Alexandre Boumezoued ,
Marc Hoffmann  and
Paulien Jeunesse
Alexandre Boumezoued*
Affiliation:
Milliman R&D, 14 Avenue de la Grande Armée, 75017Paris, France, E-mail: [email protected]
Marc Hoffmann
Affiliation:
CEREMADE, CNRS-UMR 7534, Universite Paris Dauphine, Place du maréchal de Lattre de Tassigny, 75016Paris, France, E-mail: [email protected]
Paulien Jeunesse
Affiliation:
CEREMADE, CNRS-UMR 7534, Universite Paris Dauphine, Place du maréchal de Lattre de Tassigny, 75016Paris, France, E-mail: [email protected]
*
E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We propose a new inference strategy for general population mortality tables based on annual population and death estimates, completed by monthly birth counts. We rely on a deterministic population dynamics model and establish formulas that link the death rates to be estimated with the observables at hand. The inference algorithm takes the form of a recursive and implicit scheme for computing death rate estimates. This paper demonstrates both theoretically and numerically the efficiency of using additional monthly birth counts for appropriately computing annual mortality tables. As a main result, the improved mortality estimators show better features, including the fact that previous anomalies in the form of isolated cohort effects disappear, which confirms from a mathematical perspective the previous contributions by Richards, Cairns et al., and Boumezoued.

Keywords

Mortality tablesgeneral populationdeath rate inferencepopulation dynamicscohort effectC020

MSC classification

Primary: 92D25: Population dynamics (general)
Secondary: 62P05: Applications to actuarial sciences and financial mathematics 62N02: Estimation
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 50 , Issue 2 , May 2020 , pp. 325 - 356
Copyright
© Astin Bulletin 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Beran, R. (1981) Nonparametric regression with randomly censored survival data. Technical Report, Univ. California, Berkeley.Google Scholar
Boumezoued, A. (2020) Improving mortality estimates with HFD fertility data. North American Actuarial Journal, 1–25.CrossRefGoogle Scholar
Boumezoued, A., Hoffmann, M. and Jeunesse, P. (2018) Statistical inference for an in-homogeneous age-structured population process. In revision. Preprint available at http://arxiv.org/abs/1903.00673.Google Scholar
Brown, R.L. (1997) Introduction to the Mathematics of Demography. USA: Society of Actuaries.Google Scholar
Brunel, E., Comte, F. and Guilloux, A. (2008) Estimation strategies for censored lifetimes with a lexis-diagram type model. Scandinavian Journal of Statistics, 35(3), 557–576.CrossRefGoogle Scholar
Cairns, A.J.G., Blake, D., Dowd, K. and Kessler, A.R. (2016) Phantoms never die: Living with unreliable population data. Journal of the Royal Statistical Society: Series A (Statistics in Society), 179(4), 975–1005.CrossRefGoogle Scholar
Clémençon, S., Chi Tran, V. and De Arazoza, H. (2008) A stochastic SIR model with contact-tracing: Large population limits and statistical inference. Journal of Biological Dynamics, 2(4), 392–414.CrossRefGoogle ScholarPubMed
Comte, F., Gaffas, S. and Guilloux, A. (2011) Adaptive estimation of the conditional intensity of marker-dependent counting processes. In Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, vol. 47, pp. 1171–1196. Institut Henri Poincaré.CrossRefGoogle Scholar
Dabrowska, D.M. (1987) Non-parametric regression with censored survival time data. Scandinavian Journal of Statistics, 14(3), 181–197.Google Scholar
Daley, D.J. and Vere-Jones, D. (2003) An Introduction to the Theory of Point Processes. Volume I: Elementary Theory and Methods of Probability and Its Applications. New York: Springer.Google Scholar
Doumic, M., Hoffmann, M., Krell, N. and Robert, L. (2015) Statistical estimation of a growth-fragmentation model observed on a genealogical tree. Bernoulli, 21(3), 1760–1799.CrossRefGoogle Scholar
HFD (2018) The Human Fertility Database. Germany and Austria: Max Planck Institute for Demographic Research and Vienna Institute of Demography. www.humanfertility.orgGoogle Scholar
HMD (2018) The Human Mortality Database. Berkeley, USA and Germany: University of California and Max Planck Institute for Demographic Research. www.mortality.org.Google Scholar
Hoffmann, M. and Olivier, A. (2016) Nonparametric estimation of the division rate of an age dependent branching process. Stochastic Processes and Their Applications, 126(5), 1433–1471.CrossRefGoogle Scholar
Keiding, N. (1990) Statistical inference in the lexis diagram. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 332(1627), 487–509.Google Scholar
Lee, R.D. and Carter, L.R. (1992) Modeling and forecasting US mortality. Journal of the American Statistical Association, 87(419), 659–671.Google Scholar
Lexis, W. (1875) Einleitung in die Theorie der Bevolkerungsstatistik. Strassburg: Triibner. Pages 5–7 translated to English by Keytz, N. and printed, with gure 1, in Mathematical Demography (ed. D. Smith & N. Keytz). Berlin: Springer (1977).Google Scholar
McKeague, I.W. and Utikal, K.J. (1990) Inference for a nonlinear counting process regression model. The Annals of Statistics, 18(3), 1172–1187.CrossRefGoogle Scholar
McKendrick, A.G. (1926) Application of mathematics to medical problems. Proceedings of the Edinburgh Mathematical Society, 54, 98–130.Google Scholar
Nielsen, J.P. and Linton, O.B. (1995) Kernel estimation in a nonparametric marker dependent Hazard model. The Annals of Statistics, 23(5), 1735–1748.CrossRefGoogle Scholar
Pitacco, E., Denuit, M. and Haberman, S. (2009) Modelling Longevity Dynamics for Pensions and Annuity Business. Oxford: Oxford University Press.Google Scholar
Renshaw, A.E. and Haberman, S. (2006) A cohort-based extension to the Lee–Carter model for mortality reduction factors. Insurance: Mathematics and Economics, 38(3), 556–570.Google Scholar
Richards, S.J. (2008) Detecting year-of-birth mortality patterns with limited data. Journal of the Royal Statistical Society: Series A (Statistics in Society), 171(1), 279–298.Google Scholar
Villegas, A.M., Kaishev, V.K. and Millossovich, P. (2018) StMoMo: An R package for stochastic mortality modeling. Journal of Statistical Software, 84(3), 1–38. doi:10.18637/jss.v084.i03.Google Scholar
Von Foerster, H. (1959) The Kinetics of Cellular Proliferation. New York: Grune & Stratton.Google Scholar
Wilmoth, J.R., Andreev, K., Jdanov, D., Glei, D.A., Boe, C., Bubenheim, M., Philipov, D., Shkolnikov, V. and Vachon, P. (2007) Methods Protocol for the Human Mortality Database. Berkeley and Rostock: University of California and Max Planck Institute for Demographic Research. http://mortality.org. [version 31/05/2007], 9, 10–11.Google Scholar