Accession Number:

ADA050362

Title:

Isotonic, Convex and Related Splines.

Descriptive Note:

Interim rept.,

Corporate Author:

NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS

Personal Author(s):

Report Date:

1977-11-01

Pagination or Media Count:

23.0

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.

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE