The Annals of Statistics

Backfitting in smoothing spline ANOVA

Zhen Luo

Full-text: Open access

Abstract

A computational scheme for fitting smoothing spline ANOVA models to large data sets with a (near) tensor product design is proposed. Such data sets are common in spatial-temporal analyses. The proposed scheme uses the backfitting algorithm to take advantage of the tensor product design to save both computational memory and time. Several ways to further speed up the backfitting algorithm, such as collapsing component functions and successive over-relaxation, are discussed. An iterative imputation procedure is used to handle the cases of near tensor product designs. An application to a global historical surface air temperature data set, which motivated this work, is used to illustrate the scheme proposed.

Article information

Source
Ann. Statist., Volume 26, Number 5 (1998), 1733-1759.

Dates
First available in Project Euclid: 21 June 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1024691355

Digital Object Identifier
doi:10.1214/aos/1024691355

Mathematical Reviews number (MathSciNet)
MR1673276

Zentralblatt MATH identifier
0929.62043

Subjects
Primary: 62G07: Density estimation 65D10: Smoothing, curve fitting 65F10: Iterative methods for linear systems [See also 65N22]
Secondary: 62H11: Directional data; spatial statistics 65U05 86A32: Geostatistics

Keywords
Gauss–Seidel algorithm tensor product design spatial-temporal analysis additive model collapsing grouping SOR global historical temperature data

Citation

Luo, Zhen. Backfitting in smoothing spline ANOVA. Ann. Statist. 26 (1998), no. 5, 1733--1759. doi:10.1214/aos/1024691355. https://projecteuclid.org/euclid.aos/1024691355


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