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

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