Discretized Laplacian Smoothing by Fourier Iviethods
نویسنده
چکیده
An approach to multi-dimensional smoothing is introduced which is based on a penalized with a modified The choice of penalty stanaard multi-dim~nsiQnal.Lapladan SQ11aI'e errQrcharacteristics at-least on the interior of hyper-rectangular~omains, which has wide restorationproblems,computar tions are carried out using fast Fourier transforms. Non-linear smoothing is accomplished by iterative application of the linear smoothing technique. The iterative procedure can be accelerated by means of preconditioned conjugate gradients. The methods are implemented in oneand two-dimensional settings. Adaptive choice of the amount of smoothing is based on approximate cross-validation type scores. Some illustrations are given relating to scatter-plot smoothing, estimation of a logistic regression surface and density estimation. The asymptotic mean square error characteristics of the linear smoother are derived and the smoothing splines even when these boundary conditions are not satisfied. Discretized Laplacian Smoothing by Fourier Methods Finbarr O'Sullivan Dept. of Biostatistics and Statistics University of Washington Seattle, WA 98195
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