A partial least squares approach for function-on-function interaction regression

A partial least squares regression is proposed for estimating the function-on-function model where a functional response and multiple predictors consist of random curves with quadratic interaction effects. The direct estimation usually an ill-posed problem. To overcome this difficulty, in practice, data that belong to infinite-dimensional space are generally projected into finite-dimensional basis functions. converted multivariate expansion coefficients. In phase method, variables approximated by function method. We show constructed via response, predictors, quadratic/interaction terms equivalent using expansions variables. From variables, we provide explicit formula estimate coefficient model. Because true forms models unspecified, propose forward procedure selection. finite sample performance method examined several Monte Carlo experiments two empirical analyses, results were found compare favorably existing