Spline Identity and Functional Partial Least-Squares Regression for Analysing Italian Poverty
摘要
The spline identity is a special spline function that facilitates desirable perturbations on a variable and particularly on a response in a regression context. By conducting these perturbations, decision-makers can explore various scenarios of different complexity, such as aiming to reduce poverty in a social context. To this end, we propose a functional regression framework using functional partial least-squares regression (FPLS). The response variable is transformed into a functional object using the identity spline, allowing scenario-based modifications through perturbations of its nodal coefficients. This method is particularly advantageous when the number of predictors exceeds the number of observations or when predictors exhibit significant correlation. In this context, we propose to transform the response variable by employing the spline identity, or more precisely, by using some variations around that function to study a new response-scenario.