Shape-restricted nonparametric regression with overall noisy measurements

Abstract

For a nonparametric regression problem with errors in variables, we consider a shape-restricted regression function estimate, which does not require the choice of bandwidth parameters. We demonstrate that this estimate is consistent for classes of regression function candidates, which are closed under the graph topology.

Keywords:

• nonparametric regression
• error in variables
• graph topology
• constrained maximum likelihood
• shape restrictions

AMS Classification :

• 62G08
• 62G20

Acknowledgements

The authors thank the anonymous referee for valuable hints and suggestions. This material is based upon work supported in part by the US Army Research Laboratory and the US Army Research Office under grant number W911NF1010246.