A new algorithm for spline smoothing based on smoothing a stochastic process. (English) Zbl 0627.65010

Kohn, Robert; Ansley, Craig F.

SIAM J. Sci. Stat. Comput. 8, 33-48 (1987).

A new efficient algorithm for optimal spline smoothing as the conditional expectation of a stochastic process observed with noise is given. It is shown how to use the algorithm to estimate the smoothness parameter and how to obtain Bayesian confidence intervals for the unknown function and its derivatives. Algorithms based on other stochastic models are compared.

Reviewer: G.Ya.Seliger

MSC:

65D10	Numerical smoothing, curve fitting
65C99	Probabilistic methods, stochastic differential equations
65D07	Numerical computation using splines
62F15	Bayesian inference

Keywords:

cross validation; Kalman filter; maximum likelihood; fixed interval smoothing; efficient algorithm; optimal spline smoothing; stochastic process; Bayesian confidence intervals