LAUSR

Functional data such as curves, shapes, and manifolds have become more and more common with modern technological advancements. The multiplicative regression model is well suited for analyzing data with positive responses. In this study, we study the estimation problems of the partial functional multiplicative regression model (PFMRM) based on the least absolute relative error (LARE) criterion and least product relative error (LPRE) criterion. The functional predictor and slope function are approximated by the functional principal component basis functions. Under certain regularity conditions, we derive the convergence rate of the slope function and establish the asymptotic normality of the slope vector for two estimation methods. Monte Carlo simulations are carried out to evaluate the proposed methods, and an application to Tecator data is investigated for illustration.