Skip to main content
SpringerLink
Log in

Spline interpolation for demographic variables: The monotonicity problem

  • Published:
Journal of Population Research Aims and scope Submit manuscript

Abstract

In demography, it is often necessary to obtain a monotonic interpolation of data. A solution to this problem is available using the Hyman filter for cubic splines. However, this does not seem to be well known amongst demographers, and no implementation of the procedure is readily available. We remedy these problems by outlining the relevant ideas here, and providing a function for the R language.

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

  • Brown, H.P. and A.R. Hall. 1978.Australian Demographic Databank, Volume I: Recorded Vital Statistics 1921–1976. Volume II: Population Estimates and Demographic Rates 1921–1976. Canberra: Department of Economics, Research School of Social Sciences, The Australian National University.

    Google Scholar 

  • Dalgaard, P. 2002.Introductory Statistics with R.. New York: Springer.

    Google Scholar 

  • Dougherty, R.L., A. Edelman and J.M. Hyman. 1989. Nonnegativity-, monotonicity-, or convexity-preserving cubic and quintic Hermite interpolation.Mathematics of Computation 52: 471–494.

    Article  Google Scholar 

  • Hyman, J.M. 1983. Accurate monotonicity preserving cubic interpolation.SIAM Journal on Scientific Computing 4(4): 645–654.

    Article  Google Scholar 

  • Krishnamoorthy, S. and B. Derrick. 1983.Australian Demographic Databank, Volume III: Recorded Vital Statistics, Population Estimates and Demographic Rates 1976–1981. Canberra: Department of Demography, Research School of Social Sciences, The Australian National University.

    Google Scholar 

  • Maindonald, J. and J. Braun. 2003.Data Analysis and Graphics using R: An Example-based Approach. Cambridge: Cambridge University Press.

    Google Scholar 

  • McNeil, D.R., T.J. Trussell and J.C. Turner. 1977. Spline interpolation of demographic data.Demography 14(2): 245–252.

    Article  Google Scholar 

  • Wilmoth, J.R. 2002. Methods protocol for the human mortality database, revised 1 October 2002. http://www.mortality.org/.Accessed 11 November 2003.

Download references

Author information

Authors and Affiliations

  1. Monash University, Melbourne, Australia

    Rob J. Hyndman

  2. The University of Glasgow, Glasgow, UK

    Simon N. Wood

  3. Australian Centre for Population Research, The Australian National University, 0200, ACT, Australia

    Len Smith

Authors
  1. Len Smith
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rob J. Hyndman
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Simon N. Wood
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Len Smith.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Smith, L., Hyndman, R.J. & Wood, S.N. Spline interpolation for demographic variables: The monotonicity problem. Journal of Population Research 21, 95–98 (2004). https://doi.org/10.1007/BF03032212

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03032212

Keywords

Search

Navigation