@inproceedings{63f910dcb774462bb11454a0d245eac0,

title = "On robust recursive nonparametric curve estimation",

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.",

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",

}