For nonparametric regression estimation on a bounded interval, optimal rates of decrease for integrated mean square error are known but not the best possible constants. A sharp result on such a constant, i.e., an analog of Fisher's bound for asymptotic variances is obtained for minimax risk over a Sobolev smoothness class. Normality of errors is assumed. The method is based on applying a recent result on minimax filtering in Hilbert space. A variant of spline smoothing is developed to deal with noncircular models.
Publié le : 1985-09-14
Classification:
Smooth nonparametric regression,
asymptotic minimax risk,
linear spline estimation,
boundary effects,
62G20,
62G05,
41A15,
65D10
@article{1176349651,
author = {Nussbaum, Michael},
title = {Spline Smoothing in Regression Models and Asymptotic Efficiency in $L\_2$},
journal = {Ann. Statist.},
volume = {13},
number = {1},
year = {1985},
pages = { 984-997},
language = {en},
url = {http://dml.mathdoc.fr/item/1176349651}
}
Nussbaum, Michael. Spline Smoothing in Regression Models and Asymptotic Efficiency in $L_2$. Ann. Statist., Tome 13 (1985) no. 1, pp. 984-997. http://gdmltest.u-ga.fr/item/1176349651/