COMPSTAT 2016: Start Registration
View Submission - CRoNoS FDA 2016
A0210
Title: Bootstrap in separable Hilbert spaces with applications to functional data analysis Authors:  Gil Gonzalez-Rodriguez - University of Oviedo (Spain) [presenting]
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.The aim is to illustrate how to derive consistent bootstrap approaches in separable Hilbert spaces. Naive bootstrap, bootstrap with arbitrary sample size, wild bootstrap, and several weighted bootstrap methods,including, e.g., double bootstrap, and bootstrap generated by deterministic weights, with the particular case of delete$-h$ jackknife,will be obtained as examples within the considered framework. The main results concern the bootstrapped sample mean, however since many frequent statistics can be written in terms of means by considering suitable spaces, the applicability is notable. An illustration to show how to employ the approach in the context of a functional regression problem is discussed.