It is well-known that in penalty function smoothing, the choice of tuning constant is crucial to performance. However, this has to be an intrinsically difficult problem, because, typically, the roughness penalty is an ad hoc addition to a model-based objective function (such as likelihood or least squares), and there is no defined notion of the underlying true value of h. The development of various methods proposed to estimate h has shown considerable ingenuity, for example cross-validation, or the partially Bayesian analyses of random effects models; but, necessarily, such methods operate outside the model. In this talk, an attempt is made to operate inside the model, by utilising a traditional non-parametric approach, of proposing a naive but intuitively reasonable measure for assessing the extent of smoothing imposed by any h value. For the simple case of linear smoothing splines it is shown that this measure, of Cramer-von Mises form, is proportional to the roughness penalty, and so appears to be intrinsic to the problem in a natural way. The value of h is chosen by constraining this measure to be equal to its null mean. Computational properties are regular and reliable. Possibilities of extensions to more complicated smoothing situations, and other related problems, will be discussed. 

About the speaker: Bruce Brown is Professor at the University of New South Wales. He is interested in nonparametric statistics, categorical choice models, and statistics in finance.


Professor Bruce Brown

Research Area

Statistics Seminar




Fri, 20/03/2009 - 4:00pm