Let $S^d_k$ be the set of $d$th order splines on $\lbrack 0, 1 \rbrack$ having $k$ knots $\xi_1 < \xi_2 \cdots < \xi_k$. We consider the estimation of a sufficiently smooth response function $g$, using $n$ uncorrelated observations, by an element $s$ of $S^d_k$. For large $n$ and $k$ we have discussed the asymptotic behavior of the integrated mean square error (IMSE) for two types of estimators: (i) the least squares estimator and (ii) a bias minimizing estimator. The asymptotic expression for IMSE is minimized with respect to three variables. (i) the allocation of observation (ii) the displacement of knots $\xi_1 < \cdots < \xi_k$ and (iii) number of knots.
@article{1176345203,
author = {Agarwal, Girdhar G. and Studden, W. J.},
title = {Asymptotic Integrated Mean Square Error Using Least Squares and Bias Minimizing Splines},
journal = {Ann. Statist.},
volume = {8},
number = {1},
year = {1980},
pages = { 1307-1325},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345203}
}
Agarwal, Girdhar G.; Studden, W. J. Asymptotic Integrated Mean Square Error Using Least Squares and Bias Minimizing Splines. Ann. Statist., Tome 8 (1980) no. 1, pp. 1307-1325. http://gdmltest.u-ga.fr/item/1176345203/