CREATES lunch seminar: Anders Bredahl Kock

Abstract
This paper consider penalized empirical loss minimization of convex loss functions with unknown nonlinear targets. Using the elastic net penalty we establish a finite sample oracle inequality which upper bounds the loss of our estimator with high probability. If the unknown target is linear this inequality also provides an upper bound of the estimation error of the estimated parameter vector. Next, we use the non-asymptotic results to show that the excess loss of our estimator is asymptotically of the same order as that of the oracle. If the target is linear we give sufficient conditions for consistency of the estimated parameter vector. Next, a thresholded version of our estimator is shown to be able to perform consistent variable selection. We give two examples of loss functions covered by our framework and show how nonparametric series estimation is contained as a special case and provide a finite sample upper bound on the mean square error of the elastic net series estimator. Some simulations illustrate the finite sample bounds.

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CREATES arranges lunch seminars on a regular basis, normally on Tuesdays. The speakers are usually CREATES members, mostly PhD-students and postdocs. The speakers can also be visiting PhD-students or professors.

Each lunch seminar is followed by a discussion of the paper presented.

Organizers: Anders Bredahl Kock and Cristina Amado.

Place: CREATES meeting room, M303, building 2628 (M)

www.creates.au.dk