Stochastic error analysis of spline approximation

In order to use traditional spline approximation error bounds, one needs at the very least a tight upper bound on sume nonlinear functional of the unknown function producing the data. In most practical problems, however, this information is not available, and thus these bounds cannot be computed. The most one can do in this situation is bound a normalized error. This computable upper bound is in fact the mean-square error of an associated least-squares estimation problem whose statistics are determined by the type of spline used. The bound is independent of the data and can thus be used to develop optimal sampling schemes.