Aggregation of penalized empirical risk minimizers in regression

Details Aggregation of penalized empirical risk minimizers in regression Aggregation of penalized empirical risk minimizers in regression

2008-10-29

arxiv.org/abs/0810.5288v1

Mathematics

Statistics Theory

39 pages, 5 figures

Scientific paper

We give a general result concerning the rates of convergence of penalized empirical risk minimizers (PERM) in the regression model. Then, we consider the problem of agnostic learning of the regression, and give in this context an oracle inequality and a lower bound for PERM over a finite class. These results hold for a general multivariate random design, the only assumption being the compactness of the support of its law (allowing discrete distributions for instance). Then, using these results, we construct adaptive estimators. We consider as examples adaptive estimation over anisotropic Besov spaces or reproductive kernel Hilbert spaces. Finally, we provide an empirical evidence that aggregation leads to more stable estimators than more standard cross-validation or generalized cross-validation methods for the selection of the smoothing parameter, when the number of observation is small.

Affiliated with

Also associated with

No associations

Rating

Aggregation of penalized empirical risk minimizers in regression 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 Aggregation of penalized empirical risk minimizers in regression, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Aggregation of penalized empirical risk minimizers in regression will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-72356