Estimation of Probability Density Functions for the Higgs search

This note presents some investigations of smoothing routines for the estimation of PDF, specifically the HBOOK SMOOTH, MLP-fit and a Gaussian Kernel estimator. It presents some tests on the over-training, or more generally the accuracy of the PDF. No technique is perfect, but the kernel estimator gives the best results in a series of tests, and it is recommended that it be tried for the Higgs search. Over-training is kept at a low level and the results remain reasonable at all times. It should therefore not be necessary to provide separate test and training data sets on a routine basis. Some appendices investigate how the performance depends upon the kernel width, the number of bins and the simulated statistics.