Asymptotics for polynomial spline regression under weak conditions

Jianhua Z.\ Huang

Abstract:

We derive rate of convergence for spline regression under weak conditions.
The results improve upon those in Huang (Ann. Statist, 1998) in two ways.
Firstly, results are obtained under less stringent conditions on the growing 
rate of the number of knots. Secondly, $L_2$ approximation instead of 
$L_\infty$ 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.