The Annals of Statistics

Stochastic Interpretations and Recursive Algorithms for Spline Functions

Howard L. Weinert and Thomas Kailath

Full-text: Open access

Abstract

Spline functions, which are solutions to certain deterministic optimization problems, can also be regarded as solutions to certain stochastic optimization problems; in particular, certain linear least-squares estimation problems. Such an interpretation leads to simple recursive algorithms for interpolating and smoothing splines. These algorithms compute the spline using one data point at a time, and are useful in real-time calculations when data are acquired sequentially.

Article information

Source
Ann. Statist., Volume 2, Number 4 (1974), 787-794.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176342765

Digital Object Identifier
doi:10.1214/aos/1176342765

Mathematical Reviews number (MathSciNet)
MR384290

Zentralblatt MATH identifier
0287.65009

JSTOR
links.jstor.org

Keywords
62 85 65 20 Spline functions $Lg$-splines recursive spline interpolation recursive spline smoothing stochastic interpretation least-squares estimation reproducing kernel Hilbert space

Citation

Weinert, Howard L.; Kailath, Thomas. Stochastic Interpretations and Recursive Algorithms for Spline Functions. Ann. Statist. 2 (1974), no. 4, 787--794. doi:10.1214/aos/1176342765. https://projecteuclid.org/euclid.aos/1176342765


Export citation