Spline identity and functional partial least-squares regression for analysing Italian poverty

Functional regression is a statistical technique employed to analyse the dependence between a response and a set of predictor variables both represented as functions. The functional partial least-squares regression, FPLS, constitutes a variant of functional regression analysis, proving especially advantageous when the number of predictors exceeds the number of observations or when predictors exhibit substantial correlation. Here, the particular FPLS that we call FPLSS is characterized by the use spline functions that are linear combinations of B-splines bases. To transform a response variable, we utilize a special spline function known as the identity spline, or more precisely, variations around that function, thereby controlling local changes in the observed values. This new way of exploiting the identity spline, applied here in linear or nonlinear PLS, is also applicable to any other statistical regression method. Decision-makers can then easily investigate a range of response scenarios, and particularly, use it to mitigate poverty within a social context.