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 Yand only a panel Z 1…Z L of noisy observations of X are observable. Assuming an iid. sample of (Y,Z 1…Z L) we derive in terms of both, the sample size and the panel size, a lower bound of a maximal weigthed 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. In: Ferraty, F. (eds) Recent Advances in Functional Data Analysis and Related Topics. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2736-1_7
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DOI: https://doi.org/10.1007/978-3-7908-2736-1_7
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