Recursive bias estimation for high dimensional regression smoothers

Journal Article · Thu Jan 01 04:00:00 EST 2009 · Annals of Statistics

OSTI ID:962357

Hengartner, Nicolas W ^[1]; Cornillon, Pierre - Andre ^[2]; Matzner - Lober, Eric ^[3]

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1. Los Alamos National Laboratory
2. AGROSUP, FRANCE
3. UNIV OF RENNES, FRANCE

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 L{sub 2}-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({nu}) (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.

• Research Organization: Los Alamos National Laboratory (LANL)
• Sponsoring Organization: DOE
• DOE Contract Number: AC52-06NA25396
• OSTI ID: 962357
• Report Number(s): LA-UR-09-01573; LA-UR-09-1573
• Journal Information: Annals of Statistics, Journal Name: Annals of Statistics
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
CONVERGENCE
FOCUSING
PLATES
ROUGHNESS