题目：Simultaneous white noise models and optimal recovery of functional data

嘉宾：姚方 教授（加拿大多伦多大学统计系）

时间：2015年4月30日16:00-17:00

地点：管理科研楼10楼1018会议室

单位：管理学院统计与金融系

摘要：
We consider independent and identically distributed realizations of a Gaussian process, and the observed data consist of discrete and noisy samplings of these realizations with the goal of optimally recovering the underlying trajectories. Under general conditions on both design and process, an asymptotic equivalence, in Le Cam’s sense, is established between an experiment which simultaneously describes such realizations and a collection of white noise models. In this context, the white noise models are projected onto a basis satisfying mild conditions in relation to the covariance kernel of the underlying process. This reduces the problem of initial interest to recovering coefficients in a collection of Gaussian sequence models. A variant of Stein estimation is proposed, and a key inequality is derived showing that the corresponding risks, conditioned on the underlying coefficients, can be made arbitrarily close to those that an oracle with knowledge of the covariance kernel would attain. This establishes various notions of optimality for our recovery procedure.  Finally, rigorous guarantees are derived for practically implementable procedures and empirical performance is illustrated through simulated and real data examples.