Asymptotic Equivalence and Adaptive Recovery of Functional Data

• Activity Number: 203
• Type: Invited
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: SSC
• Author(s): Fang Yao*+ and Mark Koudstaal
• Companies: University of Toronto and University of Toronto
• Keywords: Asymptotic equivalence ; Functional data ; Oracle inequality ; Stein estimation ; White noise

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 white noise model. 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, can be made arbitrarily close to those that an oracle with knowledge of the process would attain. In contrast to traditional nonparametric approaches, we are able to adapt to the smoothness regularity of the underlying process under mild assumptions.