On robust recursive nonparametric curve estimation

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

    Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer 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.
    Originele taal-2Engels
    TitelHigh dimensional probability, II (2nd International Conference, Seattle WA, USA, August 1-6, 1999)
    RedacteurenE. Giné, D.A. Mason, J.A. Wellner
    Plaats van productieBoston MA
    UitgeverijBirkhäuser Verlag
    ISBN van geprinte versie0-8176-4160-2
    StatusGepubliceerd - 2000

    Publicatie series

    NaamProgress in Probability
    ISSN van geprinte versie1050-6977


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