Estimating smooth monotone functions

J. O. Ramsay

Journal of the Royal Statistical Society Series B, 1998, vol. 60, issue 2, 365-375

Abstract: Many situations call for a smooth strictly monotone function f of arbitrary flexibility. The family of functions defined by the differential equation D 2f =w Df, where w is an unconstrained coefficient function comprises the strictly monotone twice differentiable functions. The solution to this equation is f = C0 + C1 D−1{exp(D−1w)}, where C0 and C1 are arbitrary constants and D−1 is the partial integration operator. A basis for expanding w is suggested that permits explicit integration in the expression of f. In fitting data, it is also useful to regularize f by penalizing the integral of w2 since this is a measure of the relative curvature in f. Applications are discussed to monotone nonparametric regression, to the transformation of the dependent variable in non‐linear regression and to density estimation.

Date: 1998
References: Add references at CitEc
Citations: View citations in EconPapers (56)

Downloads: (external link)
https://doi.org/10.1111/1467-9868.00130

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:jorssb:v:60:y:1998:i:2:p:365-375

Ordering information: This journal article can be ordered from
http://ordering.onli ... 1111/(ISSN)1467-9868

Access Statistics for this article

Journal of the Royal Statistical Society Series B is currently edited by P. Fryzlewicz and I. Van Keilegom

More articles in Journal of the Royal Statistical Society Series B from Royal Statistical Society Contact information at EDIRC.
Bibliographic data for series maintained by Wiley Content Delivery ().