Article révisé par les pairs
| Résumé : | We investigate a multivariate Hilbertian additive model in which the response variable is Hilbert-space-valued and predictors are multi-dimensional Euclidean. We allow for the scenario where both variables are unobservable but they are estimable. This scenario includes the case of principal or singular component scores, the case of density-valued responses and the case of semiparametric regression. For such cases, we provide estimation errors for the variables, which are of importance in their own right. Additionally, we derive the full non-asymptotic and asymptotic properties of our regression estimator under such estimation errors. This allows us to handle various novel regression problems. We demonstrate the strong performance of our regression estimator via simulation studies and a real data application. |
