Date: 2015-01-16

Time: 15:30-16:30

Location: BURN 1205

Abstract:

We consider the white noise representation of functional data taken as i.i.d. realizations of a Gaussian process. The main idea is to establish an asymptotic equivalence in Le Cam’s sense between an experiment which simultaneously describes these realizations and a collection of white noise models. In this context, we project onto an arbitrary basis and apply a novel variant of Stein-type estimation for optimal recovery of the realized trajectories. A key inequality is derived showing that the corresponding risks, conditioned on the underlying curves, are minimax optimal and can be made arbitrarily close to those that an oracle with knowledge of the process would attain. Empirical performance is illustrated through simulated and real data examples.

Speaker

Fang Yao is a Professor in the Department of Statistics at the University of Toronto. He is the 2014 recipient of the CRM-SSC Prize.