A STOCHASTIC ESTIMATOR OF THE TRACE OF THE INFLUENCE MATRIX FOR LAPLACIAN SMOOTHING SPLINES

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 is similar to one recently developed by Girard but 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 values 1, -1 each with probability 1/2. Bounds on the variance of the estimator, similar to those established by Girard, are obtained using elementary methods. The estimator can be used to approximately minimize generalised cross validation (GCV) when using. © 1990, Taylor & Francis Group, LLC. All rights reserved.