CLT in Functional Linear Regression Models

Details CLT in Functional Linear Regression Models CLT in Functional Linear Regression Models

2005-08-03

arxiv.org/abs/math/0508073v1

Mathematics

Statistics Theory

Scientific paper

We propose in this work to derive a CLT in the functional linear regression model to get confidence sets for prediction based on functional linear regression. The main difficulty is due to the fact that estimation of the functional parameter leads to a kind of ill-posed inverse problem. We consider estimators that belong to a large class of regularizing methods and we first show that, contrary to the multivariate case, it is not possible to state a CLT in the topology of the considered functional space. However, we show that we can get a CLT for the weak topology under mild hypotheses and in particular without assuming any strong assumptions on the decay of the eigenvalues of the covariance operator. Rates of convergence depend on the smoothness of the functional coefficient and on the point in which the prediction is made.

Affiliated with

Also associated with

No associations

Rating

CLT in Functional Linear Regression Models 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 CLT in Functional Linear Regression Models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and CLT in Functional Linear Regression Models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-40322