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Title: A specification test for the single functional index model Authors:  Kwo Lik Lax Chan - Università degli Studi del Piemonte Orientale (Italy) [presenting]
Abstract: The problem of specifying the link function that models the dependence structure between two random elements is a very important task in regression analysis. In the framework of scalar on-function regression, the link function is described through a real-valued operator acting on a functional space, and it is difficult to visualise and hence select a coherent specification. A test for specification in such a framework that exploits semi-parametric principles is illustrated, in particular by exploiting the Single Functional Index Model. The test statistic is a special form of U-statistic, and once it is defined, its asymptotic null distribution is derived under suitable conditions. The finite sample performances of the test are analyzed through a simulation study by using both the asymptotic p-value and some bootstrap approaches. To demonstrate the potentialities of the method, an application to a spectrometric real dataset is performed.