Title: Consistent bootstrap procedures for testing on the coefficients of a Hilbert-valued regression model
Authors: Gil Gonzalez-Rodriguez - University of Oviedo (Spain) [presenting]
Ana Colubi - Justus Liebig University Giessen (Germany)
Abstract: A convenient mathematical framework to deal with general random elements is a separable Hilbert space. This is the case, in many situations, of functional-valued random variables considered in functional data analysis. In this framework non-parametric techniques are specially useful due to the scarcity of parametric distributions. Particularly, bootstrap has proved to be highly valuable to develop inferential procedures. A quite general methodology to theoretically prove the consistency of many bootstrap approaches for random elements taking values in separable Hilbert spaces has been recently introduced. Within this context, a linear regression model with real-valued explanatory variables and Hilbert-valued coefficients and response will be considered. Several bootstrap procedures will be proposed to test about general combinations of the coefficients of this model. Its consistency will be proved by applying the general methodology.