On the effect of noisy observations of the regressor in a functional linear model

Bereswill, Mareike;Johannes, Jan
(2011)

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  • Bereswill, MareikeRuprecht-Karls Universität Heidelberg
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  • Johannes, JanUCLouvain
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Abstract
We consider the estimation of the slope function in functional linear regression, where a scalar response Y is modeled in dependence of a random function X, when Y and only a panel Z1,…., ZL of noisy observations of X are observable. Assuming an iid. sample of (Y; Z1,…, ZL) we derive in terms of both, the sample size and the panel size, a lower bound of a maximal weighted risk over certain ellipsoids of slope functions. We prove that a thresholded projection estimator can attain the lower bound up to a constant.
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Bereswill, M., & Johannes, J. (2011). On the effect of noisy observations of the regressor in a functional linear model (ISBA Discussion Paper 2011/39). https://hdl.handle.net/2078.5/209128