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We consider the statistical experiment of functional linear regression (FLR).Furthermore, we introduce a white noise model where one observes an Itoprocess, which contains the covariance operator of the corresponding FLR modelin its construction. We prove asymptotic equivalence of FLR and this whitenoise model in LeCam's sense under known design distribution. Moreover, we showequivalence of FLR and an empirical version of the white noise model for finitesample sizes. As an application, we derive sharp minimax constants in the FLRmodel which are still valid in the case of unknown design distribution.

Asymptotic equivalence of functional linear regression and a white noise inverse problem