Skip to main content
SpringerLink
Log in

Optimal Marriage Fitting for Imperfect Statistics

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

The reconstruction of the marriage market from imperfect records is solved by the minimization of a distance to the observations under civil status-specific McKendrick dynamics. To do this, the completion each year of the distribution of ages of bride and groom is also obtained by minimization under the constraints of recorded table margins, avoiding the recourse to ad hoc stylized functions. An empirical case study is presented using data from an administrative subdivision in southern Russia for the period 1867–1916.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bonneuil, N., Fursa, E.: Optimal population path fitting for flawed vital statistics and censuses. J. Optim. Theory Appl. 148, 301–317 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  2. McFarland, D.D.: Comparison of alternative marriage models. In: Greville, T.N.T. (ed.) Population Dynamics, pp. 89–106. Academic Press, New York (1972)

    Google Scholar 

  3. Martcheva, M., Milner, F.A.: The mathematics of sex and marriage. Math. Popul. Stud. 9–2, 123–142 (2001)

    Article  Google Scholar 

  4. Pollak, R.A.: Two-sex demographic models. J. Polit. Econ. 98, 399–420 (1990)

    Article  Google Scholar 

  5. Inaba, H.: Human population reproduction via first marriage. Math. Popul. Stud. 5–2, 123–144 (1995)

    Article  Google Scholar 

  6. Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220, 671–680 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  7. Otten, R.H.J.M., van Ginneken, L.P.P.P.: The Annealing Method. Kluwer, Boston (1989)

    Google Scholar 

  8. Press, W.H., Flannery, B.P., Teukolky, S.A., Vetterling, W.T.: Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press, Cambridge (1988, 1992)

    MATH  Google Scholar 

  9. Tao, P.D., An, L.T.H.: DC optimization algorithms for solving the trust region subproblem. SIAM J. Optim. 8, 476–505 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  10. Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., Teller, E.: Equation of state calculation by fast computing machines. J. Chem. Phys. 21, 1087–1092 (1953)

    Article  Google Scholar 

  11. Coale, A.J.: The decline of fertility in Europe from the French revolution to World War II. In: Behrman, S.J. et al. (eds.) Fertility and Family Planning: a World View. University of Michigan Press, Ann Arbor (1969)

    Google Scholar 

  12. Bonneuil, N.: Transformation of the French Demographic Landscape, 1806–1906. Oxford University Press, Oxford (1997)

    Google Scholar 

  13. Visnevskij, A.G. (ed.): Bracnost’, Rocdaemost’, Smertnost’v Rossii i v SSSR (Nuptiality, Natality, and Mortality in Russia and USSR). Statistica, Moscow (1977)

    Google Scholar 

  14. Dagsvik, J., Brunborg, H., Flaaten, A.: A behavioral two-sex marriage model. Math. Popul. Stud. 9, 97–122 (2001)

    Article  MATH  Google Scholar 

  15. Roth, A.E., Sotomayor, M.A.O.: Two Sided Matching. Cambridge University Press, New York (1990)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut national d’études démographiques, 133, bld Davout, 75980, Paris cedex 20, France

    Noël Bonneuil

  2. École des hautes études en sciences sociales, 190, avenue de France, 75013, Paris, France

    Noël Bonneuil

  3. Federal University of South Russia, Rostov-on-Don, Russia

    Elena Fursa

Authors
  1. Noël Bonneuil
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Elena Fursa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Noël Bonneuil.

Additional information

Communicated by Jean-Pierre Crouzeix.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bonneuil, N., Fursa, E. Optimal Marriage Fitting for Imperfect Statistics. J Optim Theory Appl 153, 532–545 (2012). https://doi.org/10.1007/s10957-011-9970-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-011-9970-8

Keywords

Search

Navigation