Functional analysis of variance for parametric functional data

A parametric functional analysis of variance (FANOVA) is proposed to measure the functional varia- bility explained by other variables. This technique presents the advantage of using all the information in the curves, instead of some specific values on them. In particular, we refer to cases in which the functional observations belong to a parametric family of functions, whose functional form is known in advance. In this framework, the approximation of the function underlying the data is not required as in the classical functional approach. Therefore, we avoid the impact that smoothing techniques might have on FANOVA. The proposed method is applied to a real data set concerning lichen biodiversity in Liguria region, in northwestern Italy