Convergence Rates for Multivariate Smoothing Spline Functions.

摘要

Smoothing splines are used to approximate smooth functions when there are only available noisy values of the function at discrete values of the independent variables. It is shown herein that as the grid of values of the independent variables becomes denser in the region of interest, the smoothing spline estimate approaches the true function. Results on the rate of this convergence are given. Convergence of derivatives is investigated, also, but under the assumption that the region is bounded. The theory of linear elliptic partial differential equations is used extensively, along with eigenvalue approximation methods. (Author)