, Volume 47, Issue 1, pp 99-106

Smoothing noisy data with spline functions

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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.