Confidence regions for periodic functions

Abstract

A periodic function, f , for which only noisy data have been observed, is estimated by a periodic smoothing spline function, fn,m,λ A confidence region for the true function is defined in terms of the maximum absolute error, . Theoretical and Monte Carlo estimates of are compared when f is a fixed unknown function and when it can be considered to come from a certain prior distribution. Use of the prior leads to more useful theoretical results.