A0312
Title: On specifying a link function of a single functional index model
Authors: Kwo Lik Lax Chan - Universita degli Studi del Piemonte Orientale (Italy) [presenting]
Abstract: An important task in regression analysis is to choose the right specification of the link function that models the dependence structure between the random elements. A challenge arises in the framework of scalar on function regression as the link function is a real-valued operator acting on a functional space, and it is difficult to visualize and hence select a coherent specification. A specification test that uses a semi-parametric approach is proposed, in particular by exploiting the Single Functional Index Model. The test statistic is a special form of U-statistic; its asymptotic null distribution is derived under suitable assumptions, and consistency is proved for a specific class of alternatives. The finite sample performances of the test are evaluated through a simulation study using both asymptotic p-values and some bootstrap approaches. An application of the method developed to a problem commonly arises in the food industry is performed to demonstrate the potentialities of the method.
