Open Access
September, 1980 Isotonic, Convex and Related Splines
Ian W. Wright, Edward J. Wegman
Ann. Statist. 8(5): 1023-1035 (September, 1980). DOI: 10.1214/aos/1176345140

Abstract

In this paper, we consider the estimation of isotonic, convex or related functions 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, we give an existence and characterization theorem 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, we examine a regression problem and show that the isotonic-type of spline provides a strongly consistent solution. We also point out several other statistical applications.

Citation

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Ian W. Wright. Edward J. Wegman. "Isotonic, Convex and Related Splines." Ann. Statist. 8 (5) 1023 - 1035, September, 1980. https://doi.org/10.1214/aos/1176345140

Information

Published: September, 1980
First available in Project Euclid: 12 April 2007

zbMATH: 0453.62036
MathSciNet: MR585701
Digital Object Identifier: 10.1214/aos/1176345140

Subjects:
Primary: 62G05
Secondary: 06A10 , 62M15 , 65D05 , 65D10

Keywords: convex , interpolating spline , Isotone , isotonic , isotonic spline , partial order , regression , smoothing spline , Spline , strong consistency

Rights: Copyright © 1980 Institute of Mathematical Statistics

Vol.8 • No. 5 • September, 1980
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