On robust recursive nonparametric curve estimation

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

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review


    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 languageEnglish
    Title of host publicationHigh dimensional probability, II (2nd International Conference, Seattle WA, USA, August 1-6, 1999)
    EditorsE. Giné, D.A. Mason, J.A. Wellner
    Place of PublicationBoston MA
    PublisherBirkhäuser Verlag
    ISBN (Print)0-8176-4160-2
    Publication statusPublished - 2000

    Publication series

    NameProgress in Probability
    ISSN (Print)1050-6977


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