A Multivariate Adaptive Data Fitting Algorithm

摘要

A method for solving the problem of approximating a discrete set of points in a multivariate setting using adaptive approximating families is presented. The user has to make a choice of the approximating family, the norm, and make assumptions about the distribution of errors. The criterion for selecting the best from the set of possible approximations is simple to apply and is derived from information-theoretic considerations. It is shown that under certain restrictive assumptions this method and that of generalized cross-validation are asymptotically equivalent. Numerical results are given to support the validity of the method.