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