# On robust recursive nonparametric curve estimation

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-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 High dimensional probability, II (2nd International Conference, Seattle WA, USA, August 1-6, 1999) E. Giné, D.A. Mason, J.A. Wellner Boston MA Birkhäuser Verlag 391-403 0-8176-4160-2 Published - 2000

### Publication series

Name Progress in Probability 47 1050-6977

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