On robust recursive nonparametric curve estimation

E. Belitser; S.A. Geer, van de

On robust recursive nonparametric curve estimation

E. Belitser
, S.A. Geer, van de

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

The authors consider the problem of estimating a regression function $\theta\colon \ [0,1]\rightarrow{\bf R}$ when moments of the estimation errors may not exist. More specifically, $\theta$ is assumed to lie in some class $\Theta_\beta$ of Lipschitz functions with smoothness $\beta.$ The distribution of the i.i.d. error terms is assumed to have zero median and a Lipschitz continuous density that is bounded away from zero in some interval around zero. The design is assumed to be almost equidistant. For the problem, a robust recursive estimate is proposed that is based on a stochastic approximation procedure. The rate of uniform (over both $\Theta_\beta$ and a suitable subset of $[0,1]$) convergence is derived for the estimate.

Original language	English
Title of host publication	High dimensional probability, II (2nd International Conference, Seattle WA, USA, August 1-6, 1999)
Editors	E. Giné, D.A. Mason, J.A. Wellner
Place of Publication	Boston MA
Publisher	Birkhäuser Verlag
Pages	391-403
ISBN (Print)	0-8176-4160-2
Publication status	Published - 2000

Publication series

Name	Progress in Probability
Volume	47
ISSN (Print)	1050-6977

Cite this

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title = "On robust recursive nonparametric curve estimation",

abstract = "The authors consider the problem of estimating a regression function \$\textbackslash{}theta\textbackslash{}colon \textbackslash{} [0,1]\textbackslash{}rightarrow\{\textbackslash{}bf R\}\$ when moments of the estimation errors may not exist. More specifically, \$\textbackslash{}theta\$ is assumed to lie in some class \$\textbackslash{}Theta\_\textbackslash{}beta\$ of Lipschitz functions with smoothness \$\textbackslash{}beta.\$ The distribution of the i.i.d. error terms is assumed to have zero median and a Lipschitz continuous density that is bounded away from zero in some interval around zero. The design is assumed to be almost equidistant. For the problem, a robust recursive estimate is proposed that is based on a stochastic approximation procedure. The rate of uniform (over both \$\textbackslash{}Theta\_\textbackslash{}beta\$ and a suitable subset of \$[0,1]\$) convergence is derived for the estimate.",

author = "E. Belitser and \{Geer, van de\}, S.A.",

year = "2000",

language = "English",

isbn = "0-8176-4160-2",

series = "Progress in Probability",

publisher = "Birkh{\"a}user Verlag",

pages = "391--403",

editor = "E. Gin{\'e} and D.A. Mason and J.A. Wellner",

booktitle = "High dimensional probability, II (2nd International Conference, Seattle WA, USA, August 1-6, 1999)",

address = "Switzerland",

}

On robust recursive nonparametric curve estimation. / Belitser, E.; Geer, van de, S.A.
High dimensional probability, II (2nd International Conference, Seattle WA, USA, August 1-6, 1999). ed. / E. Giné; D.A. Mason; J.A. Wellner. Boston MA: Birkhäuser Verlag, 2000. p. 391-403 (Progress in Probability; Vol. 47).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - On robust recursive nonparametric curve estimation

AU - Belitser, E.

AU - Geer, van de, S.A.

PY - 2000

Y1 - 2000

N2 - The authors consider the problem of estimating a regression function $\theta\colon \ [0,1]\rightarrow{\bf R}$ when moments of the estimation errors may not exist. More specifically, $\theta$ is assumed to lie in some class $\Theta_\beta$ of Lipschitz functions with smoothness $\beta.$ The distribution of the i.i.d. error terms is assumed to have zero median and a Lipschitz continuous density that is bounded away from zero in some interval around zero. The design is assumed to be almost equidistant. For the problem, a robust recursive estimate is proposed that is based on a stochastic approximation procedure. The rate of uniform (over both $\Theta_\beta$ and a suitable subset of $[0,1]$) convergence is derived for the estimate.

AB - The authors consider the problem of estimating a regression function $\theta\colon \ [0,1]\rightarrow{\bf R}$ when moments of the estimation errors may not exist. More specifically, $\theta$ is assumed to lie in some class $\Theta_\beta$ of Lipschitz functions with smoothness $\beta.$ The distribution of the i.i.d. error terms is assumed to have zero median and a Lipschitz continuous density that is bounded away from zero in some interval around zero. The design is assumed to be almost equidistant. For the problem, a robust recursive estimate is proposed that is based on a stochastic approximation procedure. The rate of uniform (over both $\Theta_\beta$ and a suitable subset of $[0,1]$) convergence is derived for the estimate.

M3 - Conference contribution

SN - 0-8176-4160-2

T3 - Progress in Probability

SP - 391

EP - 403

BT - High dimensional probability, II (2nd International Conference, Seattle WA, USA, August 1-6, 1999)

A2 - Giné, E.

A2 - Mason, D.A.

A2 - Wellner, J.A.

PB - Birkhäuser Verlag

CY - Boston MA

ER -

On robust recursive nonparametric curve estimation

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