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August 2002 Application of structural risk minimization to multivariate smoothing spline regression estimates
Michael Kohler, Adam Krzyzak, Dominik Schäfer
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Bernoulli 8(4): 475-489 (August 2002).


Estimation of regression functions from bounded, independent and identically distributed data is considered. Motivated by Vapnik's principle of structural risk minimization, a data-dependent choice of the smoothing parameter of multivariate smoothing spline estimates is proposed. The corresponding smoothing spline estimates automatically adapt to the unknown smoothness of the regression function and their $L^2$ errors achieve the optimal rate of convergence up to a logarithmic factor. The result is valid without any regularity conditions on the distribution of the design.


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Michael Kohler. Adam Krzyzak. Dominik Schäfer. "Application of structural risk minimization to multivariate smoothing spline regression estimates." Bernoulli 8 (4) 475 - 489, August 2002.


Published: August 2002
First available in Project Euclid: 7 March 2004

zbMATH: 1003.62035
MathSciNet: MR2003E:62069

Keywords: Empirical process theory , rate of convergence , regression estimate , smoothing splines , structural risk minimization

Rights: Copyright © 2002 Bernoulli Society for Mathematical Statistics and Probability


Vol.8 • No. 4 • August 2002
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