Statistical Science

Monotone Regression Splines in Action

J. O. Ramsay

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Abstract

Piecewise polynomials or splines extend the advantages of polynomials to include greater flexibility, local effects of parameter changes and the possibility of imposing useful constraints on estimated functions. Among these constraints is monotonicity, which can be an important property in many curve estimation problems. This paper shows the virtues of monotone splines through a number of statistical applications, including response variable transformation in nonlinear regression, transformation of variables in multiple regression, principal components and canonical correlation, and the use of monotone splines to model a dose-response function and to perform item analysis. Computational and inferential issues are discussed and illustrated.

Article information

Source
Statist. Sci. Volume 3, Number 4 (1988), 425-441.

Dates
First available: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.ss/1177012761

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/ss/1177012761

Citation

Ramsay, J. O. Monotone Regression Splines in Action. Statistical Science 3 (1988), no. 4, 425--441. doi:10.1214/ss/1177012761. http://projecteuclid.org/euclid.ss/1177012761.


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See also

  • See Comment: Leo Breiman. [Monotone Regression Splines in Action]: Comment. Statist. Sci., Volume 3, Number 4 (1988), 442--445.
  • See Comment: Randy Eubank. [Monotone Regression Splines in Action]: Comment. Statist. Sci., Volume 3, Number 4 (1988), 446--450.
  • See Comment: Trevor Hastie, Robert Tibshirani. [Monotone Regression Splines in Action]: Comment. Statist. Sci., Volume 3, Number 4 (1988), 450--456.
  • See Comment: Grace Wahba. [Monotone Regression Splines in Action]: Comment. Statist. Sci., Volume 3, Number 4 (1988), 456--458.
  • See Comment: J. O. Ramsay. [Monotone Regression Splines in Action]: Rejoinder. Statist. Sci., Volume 3, Number 4 (1988), 459--461.