Skip to main content

Spline Functions

  • Reference work entry
  • First Online:

Abstract

Spline functions are smooth piecewise functions that are popular tools in approximation theory and which arise naturally in economics.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   6,499.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   8,499.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Bibliography

  • Craven, P., and G. Wahba. 1979. Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of cross-validation. Numerische Mathematik 31: 377–403.

    Article  Google Scholar 

  • De Boor, C. 2001. A practical guide to splines. New York: Springer-Verlag.

    Google Scholar 

  • Denison, D., B. Mallick, and A. Smith. 1998. Automatic Bayesian curve fitting. Journal of the Royal Statistical Society: Series B 60: 333–350.

    Article  Google Scholar 

  • DiMatteo, I., C. Genovese, and R. Kass. 2001. Bayesian curve-fitting with free knot splines. Biometrika 88: 1055–1071.

    Article  Google Scholar 

  • Eubank, R. 1988. Spline smoothing and nonparametric regression. New York: Marcel Dekker.

    Google Scholar 

  • Friedman, J., and B. Silverman. 1989. Flexible parsimonious smoothing and additive modeling. Technometrics 31: 3–21.

    Article  Google Scholar 

  • Green, P., and B. Silverman. 1994. Nonparametric regression and generalized linear models. London: Chapman and Hall.

    Book  Google Scholar 

  • Halpern, E. 1973. Bayesian spline regression when the number of knots is unknown. Journal of the Royal Statistical Society: Series B 35: 347–360.

    Google Scholar 

  • Hansen, M., C. Kooperberg, and S. Sardy. 1998. Triogram models. Journal of the American Statistical Association 93: 101–119.

    Article  Google Scholar 

  • Kimeldorf, G., and G. Wahba. 1970. A correspondence between Bayesian estimation on stochastic processes and smoothing by splines. Annals of Mathematical Statistics 41: 495–502.

    Article  Google Scholar 

  • Poirier, D. 1976. The econometrics of structural change with special emphasis on spline functions. Amsterdam: North-Holland.

    Google Scholar 

  • Schoenberg, I. 1946. Contributions to the problem of approximation of equidistant data by analytic functions: Parts I and II. Quarterly Journal of Applied Mathematics 4 (45–99): 112–141.

    Article  Google Scholar 

  • Schumaker, L. 1981. Spline functions: Basic theory. New York: Wiley.

    Google Scholar 

  • Silverman, B. 1985. Some aspects of the spline smoothing approach to nonparametric regression curve fitting (with discussion). Journal of the Royal Statistical Society: Series B 47: 1–52.

    Google Scholar 

  • Smith, M., and R. Kohn. 1996. Nonparametric regression using Bayesian variable selection. Journal of Econometrics 75: 317–343.

    Article  Google Scholar 

  • Smith, M., C. Wong, and R. Kohn. 1998. Additive nonparametric regression with autocorrelated errors. Journal of the Royal Statistical Society: Series B 60: 311–331.

    Article  Google Scholar 

  • Wahba, G. 1978. Improper priors, spline smoothing and the problem of guarding against model errors in regression. Journal of the Royal Statistical Society: Series B 40: 364–372.

    Google Scholar 

  • Wahba, G. 1983. Bayesian ‘confidence intervals’ for the cross-validated smoothing spline. Journal of the Royal Statistical Society: Series B 45: 133–150.

    Google Scholar 

  • Wahba, G. 1990. Spline models for observational data. Philadelphia: Society for Industrial and Applied Mathematics.

    Book  Google Scholar 

  • Whittaker, E. 1923. On a new method of graduation. Proceedings of the Edinburgh Mathematical Society 41: 63–75.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Copyright information

© 2018 Macmillan Publishers Ltd.

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Poirier, D.J. (2018). Spline Functions. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_1454

Download citation

Publish with us

Policies and ethics