Accuracy and efficiency of alternative spline smoothing algorithms

Abstract

Wahba (1978) showed that a smoothing spline could be obtained as the estimate of the signal in a signal plus noise model. By expressing Wahba's (1978) stochastic model in state space form we can obtain a spline smoothing algorithm which can also be used to estimate the smoothing parameter from the data by either generalized cross-validation or marginal likelihood, and to compute Bayesian confidence intervals for the unobserved function and its derivatives at all abscissae. In this paper we investigate the speed and accuracy of the state space spline smoothing algorithm and show that it compares favourably to the algorithms of Hutchinson and de Hogg (1985) and Woltring (1986). We also present a square root version of the algorithm which is numerically more accurate and is useful in the computation of higher order splines.

Keywords:

• Filtering
• Generalized cross-validation
• Marginal likelihood
• Smoothing
• State space model