报告题目：Functional Regression on Manifold with Contamination

报告时间：2017年11月2日（周四） 15:00

报告地点：统计学院办公楼1层104会议室

主讲人：姚方，多伦多大学统计科学系教授，北京大学讲席教授。主要研究方向包括无限维空间的函数型数据分析， 现阶段的研究集中在具有高维或者流形结构的函数型数据的方法和理论以及在大型复杂数据中的应用。2014年获得由加拿大统计学会和数学研究中心联合颁发的授予博士毕业15年内在加拿大做出突出贡献的统计学家的 CRM-SSC奖，2017年当选为国际数理统计学会（IMS）Fellow。担任十个国际统计学核心期刊的副主编，包括顶级期刊Journal of the American Statistical Association和 Annals of Statistics。

报告摘要：We propose a new perspective on functional regression with a predictor process via the concept of manifold that is intrinsically finite-dimensional and embedded in an infinite-dimensional functional space, where the predictor is contaminated with discrete/noisy measurements.  By a novel method of  functional local linear manifold smoothing, we achieve a polynomial rate of convergence that adapts to the intrinsic manifold dimension and the level of sampling/noise contamination with a phase transition phenomenon depending on their interplay. This is in contrast to the logarithmic convergence rate in the literature of functional nonparametric regression. We demonstrate that the proposed method enjoys favourable finite sample performance relative to commonly used methods via simulated and real data examples.