Summary
A procedure for calculating the trace of the influence matrix associated with a polynomial smoothing spline of degree2m−1 fitted ton distinct, not necessarily equally spaced or uniformly weighted, data points is presented. The procedure requires orderm 2 n operations and therefore permits efficient orderm 2 n calculation of statistics associated with a polynomial smoothing spline, including the generalized cross validation. The method is a significant improvement over an existing method which requires ordern 3 operations.
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Hutchinson, M.F., de Hoog, F.R. Smoothing noisy data with spline functions. Numer. Math. 47, 99–106 (1985). https://doi.org/10.1007/BF01389878
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DOI: https://doi.org/10.1007/BF01389878