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A stochastic estimator of the trace of the influence matrix for Laplacian smoothing splines. (English) Zbl 0718.62058
An unbiased stochastic estimator of tr(I-A), where A is the influence matrix associated with the calculation of Laplacian smoothing splines, is described. The estimator satisfies a minimum variance criterion and does not require the simulation of a standard normal variable. It uses instead simulations of the discrete random variable which takes the vaues 1, -1 each with probability 1/2. Bounds on the variance of the estimator are obtained using elementary methods. The estimator can be used to approximately minimize generalized cross validation (GCV) when using discretized iterative methods for fitting Laplacian smoothing splines to very large data sets.

MSC:
62F10 Point estimation
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