We introduce a new class of variable kernels which depend on the smoothing parameter b through a simple scaling operation, and which have good integrated mean square error (IMSE) convergence properties. These kernels deform "automatically" near the boundary, eliminating boundary bias. Computational formulas are given for all orders of kernel in terms of exponentially damped sines and cosines. The kernel is a computationally convenient approximation to a certain Green's function, with the resulting kernel estimate closely related to a smoothing spline estimate.
@article{1176349021,
author = {Messer, Karen and Goldstein, Larry},
title = {A New Class of Kernels for Nonparametric Curve Estimation},
journal = {Ann. Statist.},
volume = {21},
number = {1},
year = {1993},
pages = { 179-195},
language = {en},
url = {http://dml.mathdoc.fr/item/1176349021}
}
Messer, Karen; Goldstein, Larry. A New Class of Kernels for Nonparametric Curve Estimation. Ann. Statist., Tome 21 (1993) no. 1, pp. 179-195. http://gdmltest.u-ga.fr/item/1176349021/