Mathematics – Statistics Theory
Scientific paper
2009-02-03
Mathematics
Statistics Theory
Major revision
Scientific paper
We consider the estimation of the value of a linear functional of the slope parameter in functional linear regression, where scalar responses are modeled in dependence of random functions. The theory in this paper covers in particular point-wise estimation as well as the estimation of weighted averages of the slope parameter. We propose a plug-in estimator which is based on a dimension reduction technique and additional thresholding. It is shown that this estimator is consistent under mild assumptions. We derive a lower bound for the maximal mean squared error of any estimator over a certain ellipsoid of slope parameters and a certain class of covariance operators associated with the regressor. It is shown that the proposed estimator attains this lower bound up to a constant and hence it is minimax optimal. Our results are appropriate to discuss a wide range of possible regressors, slope parameters and functionals. They are illustrated by considering the point-wise estimation of the slope parameter or its derivatives and its average value over a given interval.
Johannes Jeff
Schenk Rudolf
No associations
LandOfFree
On rate optimal local estimation in functional linear model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On rate optimal local estimation in functional linear model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On rate optimal local estimation in functional linear model will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-553067