Asymptotics for polynomial spline regression under weak conditions
We derive rate of convergence for spline regression under weak conditions. The results improve upon those in Huang (Ann. Statist. 26 (1998a) 242) in two ways. Firstly, results are obtained under less stringent conditions on the growing rate of the number of knots. Secondly, L2 approximation instead of L[infinity] approximation by splines are used to bound the rate of convergence, this allows us to obtain results when the regression function or its components in ANOVA decomposition are in broader function classes.
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Volume (Year): 65 (2003)
Issue (Month): 3 (November)
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References listed on IDEAS
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- Huang, Jianhua Z., 1998. "Functional ANOVA Models for Generalized Regression," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 49-71, October.
- He, Xuming & Shi, Peide, 1996. "Bivariate Tensor-Product B-Splines in a Partly Linear Model," Journal of Multivariate Analysis, Elsevier, vol. 58(2), pages 162-181, August.