Summary
Analyses with smoothing splines are conveniently formalized using a reproducing kernel Hilbert space. The inner product in such a space and the corresponding reproducing kernel — given a smoothness criterion — can be defined in infinitely many ways. The smoothing spline itself is known to be independent of the choice of the inner product. Furthermore it is proven that the usual statistical inferences with smoothing splines (under different distributional 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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© 1996 Physica-Verlag Heidelberg
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van der Linde, A. (1996). The Invariance of Statistical Analyses with Smoothing Splines with Respect to the Inner Product in the Reproducing Kernel Hilbert Space. In: Härdle, W., Schimek, M.G. (eds) Statistical Theory and Computational Aspects of Smoothing. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-48425-4_12
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DOI: https://doi.org/10.1007/978-3-642-48425-4_12
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