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Backfitting in smoothing spline ANOVA. (English) Zbl 0929.62043
Summary: 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.

MSC:
62G07 Density estimation
65C60 Computational problems in statistics (MSC2010)
62H12 Estimation in multivariate analysis
65D10 Numerical smoothing, curve fitting
65F10 Iterative numerical methods for linear systems
86A32 Geostatistics
Software:
gss
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