Titlebook: Statistical Theory and Computational Aspects of Smoothing; Proceedings of the C Wolfgang Härdle,Michael G. Schimek Conference proceedings 1

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Some Comments on Cross-Validation,on approach in general regression situations. Both criteria may be regarded as estimates of the mean squared error of prediction. Under some assumptions including normally distributed observations, the cross-validation criterion is shown to be outperformed by the full cross-validation criterion. Ana

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Mean and Dispersion Additive Models,r and a known variance function of the mean. The dependence of each of the mean and dispersion parameter on explanatory variables is modelled using a semi-parametric additive model. We call this model the ’Mean and Dispersion Additive Model’ or ’MADAM’. The MADAM is fitted either by maximisation of

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Interaction in Nonlinear Principal Components Analysis,in PC A. Such algorithm fits a model in which principal components are data driven dimensionality reduction functions. The detection of meaningful interaction is a way to specify such general unknown functions. As an example the highly nonlinear structure of a circle is recovered by the first compon

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1431-1968 theoretical interest in the development of such techniques. Related algorithmic concepts have been a main concern in computational statistics. Smoothing techniques in regression as well as other statistical methods are increasingly applied in biosciences and economics. But they are also relevant for

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The Invariance of Statistical Analyses with Smoothing Splines with Respect to the Inner Product in butional assumptions leading to signal extraction, Bayesian or minimax estimation) and particularly the smoothing error are invariant w.r.t. to the choice of the inner product. For a special inner product the smoothing spline is an orthogonal projection.

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A Note on Cross-Validation for Smoothing Splines,blems of variance estimation. Two competitors for error variance estimation turn out to perform equally well, and the estimate for the variance of the Bayesian prior appears to be useful for describing the complexity of the estimated function.

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Some Comments on Cross-Validation,logous modifications may be applied to the generalized cross-validation method, providing a similar improvement. This leads to the recommendation of replacing the traditional cross-validation techniques by the new ones for estimating the prediction quality of models or of regression function estimators.