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The prediction error in functional regression

The prediction error in functional regression

This video was recorded at Workshop on Sparsity and Inverse Problems in Statistical Theory and Econometrics, Berlin 2008. The talk considers functional linear regression, where scalar responses Y are modeled in dependence of random functions. We propose a smoothing splines estimator for the functional slope parameter based on a slight modi- fication of the usual penalty. Theoretical analysis concentrates on the error in an out-of-sample prediction of the response for a new random function. It is shown that rates of convergence of the prediction error depend on the smoothness of the slope function and on the structure of the predictors. We then prove that these rates are optimal in the sense that they are minimax over large classes of possible slope functions and distributions of the predic- tive curves. For the case of models with errors-in-variables the smoothing spline estimator is modified by using a denoising correction of the covari- ance matrix of discretized curves. The methodology is then applied to a real case study where the aim is to predict the maximum of the concentration of ozone by using the curve of this concentration measured the preceding day.

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