• Bernoulli
  • Volume 8, Number 4 (2002), 475-489.

Application of structural risk minimization to multivariate smoothing spline regression estimates

Michael Kohler, Adam Krzyzak, and Dominik Schäfer

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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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Bernoulli, Volume 8, Number 4 (2002), 475-489.

First available in Project Euclid: 7 March 2004

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empirical process theory rate of convergence regression estimate smoothing splines structural risk minimization


Kohler, Michael; Krzyzak, Adam; Schäfer, Dominik. Application of structural risk minimization to multivariate smoothing spline regression estimates. Bernoulli 8 (2002), no. 4, 475--489.

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