Asymptotic equivalence of functional linear regression and a white noise inverse problem
by Alexander Meister
Abstract: We consider the statistical experiment of functional linear regression (FLR). Furthermore, we introduce a white noise model where one observes an Ito process which contains the covariance operator of the corresponding FLR model in its construction. We prove asymptotic equivalence of FLR and this white noise model in LeCam's sense.
Moreover, we show equivalence of FLR and an empirical version of the white noise model for finite sample sizes.
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