# On pointwise adaptive curve estimation based on inhomogeneous data

ESAIM: Probability and Statistics (2007)

- Volume: 11, page 344-364
- ISSN: 1292-8100

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topGaïffas, Stéphane. "On pointwise adaptive curve estimation based on inhomogeneous data." ESAIM: Probability and Statistics 11 (2007): 344-364. <http://eudml.org/doc/250082>.

@article{Gaïffas2007,

abstract = {
We want to recover a signal based on noisy inhomogeneous data (the
amount of data can vary strongly on the estimation domain). We model
the data using nonparametric regression with random design, and we
focus on the estimation of the regression at a fixed point x0
with little, or much data. We propose a method which adapts both to
the local amount of data (the design density is unknown) and to the
local smoothness of the regression function. The procedure consists
of a local polynomial estimator with a Lepski type data-driven
bandwidth selector, see for instance
Lepski et al. [Ann. Statist.25 (1997) 929–947]. We assess this procedure in the
minimax setup, over a class of function with local smoothness s >
0 of Hölder type. We quantify the amount of data at x0 in
terms of a local property on the design density called regular
variation, which allows situations with strong variations in the
concentration of the observations. Moreover, the optimality of the
procedure is proved within this framework.
},

author = {Gaïffas, Stéphane},

journal = {ESAIM: Probability and Statistics},

keywords = {Adaptive estimation; inhomogeneous data; nonparametric
regression; random design.; adaptive estimation; random design},

language = {eng},

month = {8},

pages = {344-364},

publisher = {EDP Sciences},

title = {On pointwise adaptive curve estimation based on inhomogeneous data},

url = {http://eudml.org/doc/250082},

volume = {11},

year = {2007},

}

TY - JOUR

AU - Gaïffas, Stéphane

TI - On pointwise adaptive curve estimation based on inhomogeneous data

JO - ESAIM: Probability and Statistics

DA - 2007/8//

PB - EDP Sciences

VL - 11

SP - 344

EP - 364

AB -
We want to recover a signal based on noisy inhomogeneous data (the
amount of data can vary strongly on the estimation domain). We model
the data using nonparametric regression with random design, and we
focus on the estimation of the regression at a fixed point x0
with little, or much data. We propose a method which adapts both to
the local amount of data (the design density is unknown) and to the
local smoothness of the regression function. The procedure consists
of a local polynomial estimator with a Lepski type data-driven
bandwidth selector, see for instance
Lepski et al. [Ann. Statist.25 (1997) 929–947]. We assess this procedure in the
minimax setup, over a class of function with local smoothness s >
0 of Hölder type. We quantify the amount of data at x0 in
terms of a local property on the design density called regular
variation, which allows situations with strong variations in the
concentration of the observations. Moreover, the optimality of the
procedure is proved within this framework.

LA - eng

KW - Adaptive estimation; inhomogeneous data; nonparametric
regression; random design.; adaptive estimation; random design

UR - http://eudml.org/doc/250082

ER -

## References

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