Isotonic, Convex and Related Splines.
Abstract
The estimation of isotonic, convex or related functions is considered by means of splines. It is shown that certain classes of isotone or convex functions can be represented as a positive cone embedded in a Hilbert space. Using this representation, an existence and characterization theorem are given for isotonic or convex splines. Two special cases are examined showing the existence of a globally monotone cubic smoothing spline and a globally convex quintic smoothing spline. Finally, a regression problem is examined and shows that the isotonic-type of spline provides a strongly consistent solution. Several other statistical applications are given.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1977
- Accession Number
- ADA050362
Entities
People
- Edward Wegman
- Ian W. Wright
Organizations
- University of North Carolina at Chapel Hill