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Title: Testing a functional regression model through consistent bootstrap procedures Authors:  Gil Gonzalez-Rodriguez - University of Oviedo (Spain) [presenting]
Ana Colubi - Justus Liebig University Giessen (Germany)
Abstract: Hilbert spaces are frequently used in statistics as a framework to deal with general random elements, specially with functional-valued random variables. The scarcity of common parametric distribution models in this context makes it important to develop non-parametric techniques, and among them, bootstrap has already proved to be specially valuable. A methodology to derive consistency results for some usual bootstrap methods when working in separable Hilbert spaces has been developed recently. By applying the proposed methodology, the consistency of well-known bootstrap procedures involving the sample mean as the naive bootstrap, bootstrap with arbitrary sample size, wild bootstrap, and more generally, weighted bootstrap methods, including double bootstrap and bootstrap generated by deterministic weights with the particular case of delete-h jackknife is proved. The aim is to illustrate how to employ the approach in the context of a functional regression hypothesis test.