Computing the error for smoothing splines (Q1965979)

To consider the problem of estimation the error for smoothing splines the Bayesian approach is used following the works by \textit{G. Wahba} [J. R. Stat. Soc. Ser. B 40, 364-372 (1978; Zbl 0407.62048); ibid. 45, 133-150 (1983; Zbl 0538.65006)]. The theoretical background and estimation strategies are briefly described and problems in computing Wahba's Bayesian errors are demonstrated and discussed. In order to compute the error for smoothing splines the smoothing parameter, known to be the ratio of the scale factors of the sample variance to the prior variance has to be decomposed into these factors. It is pointed out that for similar (estimated) smoothing parameters the prior scale factor may vary considerably yielding an unreliable estimate of the smoothing error.