We propose a method of adaptive estimation of a regression function
which is near optimal in the classical sense of the mean integrated error. At
the same time, the estimator is shown to be very sensitive to discontinuities
or change-points of the underlying function $f$ or its derivatives. For
instance, in the case of a jump of a regression function, beyond the intervals
of length (in order) $n^{-1} \log n$ around change-points the quality of
estimation is essentially the same as if locations of jumps were known. The
method is fully adaptive and no assumptions are imposed on the design, number
and size of jumps. The results are formulated in a nonasymptotic way and can
therefore be applied for an arbitrary sample size.
Publié le : 1998-08-14
Classification:
Change-point,
local polynomial fit,
local structure,
nonparametric regression,
pointwise adaptive estimation,
62G07,
62G20
@article{1024691246,
author = {Spokoiny, V. G.},
title = {Estimation of a function with discontinuities via local polynomial
fit with an adaptive window choice},
journal = {Ann. Statist.},
volume = {26},
number = {3},
year = {1998},
pages = { 1356-1378},
language = {en},
url = {http://dml.mathdoc.fr/item/1024691246}
}
Spokoiny, V. G. Estimation of a function with discontinuities via local polynomial
fit with an adaptive window choice. Ann. Statist., Tome 26 (1998) no. 3, pp. 1356-1378. http://gdmltest.u-ga.fr/item/1024691246/