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December, 1991 Interaction Spline Models and Their Convergence Rates
Zehua Chen
Ann. Statist. 19(4): 1855-1868 (December, 1991). DOI: 10.1214/aos/1176348374


We consider interaction splines which model a multivariate regression function $f$ as a constant plus the sum of functions of one variable (main effects), plus the sum of functions of two variables (two-factor interactions), and so on. The estimation of $f$ by the penalized least squares method and the asymptotic properties of the models are studied in this article. It is shown that, under some regularity conditions on the data points, the expected squared error averaged over the data points converges to zero at a rate of $O(N^{-2m/(2m + 1)})$ as the sample size $N \rightarrow \infty$ if the smoothing parameters are appropriately chosen, where $m$ is a measure of the assumed smoothness of $f.$


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Zehua Chen. "Interaction Spline Models and Their Convergence Rates." Ann. Statist. 19 (4) 1855 - 1868, December, 1991.


Published: December, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0738.62065
MathSciNet: MR1135152
Digital Object Identifier: 10.1214/aos/1176348374

Primary: 62H12
Secondary: 62G05 , 62G20

Keywords: kernel matrix , Prediction mean squared error , ‎reproducing kernel Hilbert ‎space

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 4 • December, 1991
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