Recursive bias estimation for high dimensional regression smoothers [electronic resource].

Published:: Washington, D.C. : United States. Dept. of Energy, 2009.
Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy.
Additional Creators:: Los Alamos National Laboratory, United States. Department of Energy, and United States. Department of Energy. Office of Scientific and Technical Information

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Summary:

In multivariate nonparametric analysis, sparseness of the covariates also called curse of dimensionality, forces one to use large smoothing parameters. This leads to biased smoother. Instead of focusing on optimally selecting the smoothing parameter, we fix it to some reasonably large value to ensure an over-smoothing of the data. The resulting smoother has a small variance but a substantial bias. In this paper, we propose to iteratively correct of the bias initial estimator by an estimate of the latter obtained by smoothing the residuals. We examine in details the convergence of the iterated procedure for classical smoothers and relate our procedure to L₂-Boosting, For multivariate thin plate spline smoother, we proved that our procedure adapts to the correct and unknown order of smoothness for estimating an unknown function m belonging to H(ν) (Sobolev space where m should be bigger than d/2). We apply our method to simulated and real data and show that our method compares favorably with existing procedures.

Report Numbers:

E 1.99:la-ur-09-01573
E 1.99: la-ur-09-1573
la-ur-09-1573
la-ur-09-01573

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Note:

Published through SciTech Connect.
01/01/2009.
"la-ur-09-01573"
" la-ur-09-1573"
Annals of Statistics FT
Hengartner, Nicolas W; Cornillon, Pierre - Andre; Matzner - Lober, Eric.

Funding Information:

AC52-06NA25396

View MARC record | catkey: 14653803