Usual nonparametric regression estimators often show many little wiggles which do not appear to be necessary for a good description of the data. The new "Wp" smoother is a maximum penalized likelihood (MPL) estimate with a novel roughness penalty. It penalizes a relative change of curvature. This leads to disjoint classes of functions, each with given number, $n_w$, of inflection points. For a "Wp" estimate, $f"(x) = \pm (x - w_1)\cdots (x - w_{n_w}) \cdot \exp h_f(x)$, which is semiparametric, with parameters $w_j$ and nonparametric part $h_f(\cdot)$. The main mathematical result is a convenient form of the characterizing differential equation for a very general class of MPL estimators.
Publié le : 1995-10-14
Classification:
Nonparametric regression,
roughness penalty,
maximum penalized likelihood,
inflection point,
robust smoothing,
62G07,
34B10,
41A29,
65D07,
65D10
@article{1176324309,
author = {Machler, Martin B.},
title = {Variational Solution of Penalized Likelihood Problems and Smooth Curve Estimation},
journal = {Ann. Statist.},
volume = {23},
number = {6},
year = {1995},
pages = { 1496-1517},
language = {en},
url = {http://dml.mathdoc.fr/item/1176324309}
}
Machler, Martin B. Variational Solution of Penalized Likelihood Problems and Smooth Curve Estimation. Ann. Statist., Tome 23 (1995) no. 6, pp. 1496-1517. http://gdmltest.u-ga.fr/item/1176324309/