講座名稱：Functional Regression on Manifold with Contamination

講座時(shí)間：2020-09-09 10:00

講座人：姚方 教授

講座地點(diǎn)：騰訊會(huì)議直播（ID：932 719 167）

講座人介紹：

姚方，北京大學(xué)博雅講席教授, 北大統(tǒng)計(jì)科學(xué)中心主任，數(shù)理統(tǒng)計(jì)學(xué)會(huì)（IMS）Fellow，美國(guó)統(tǒng)計(jì)學(xué)會(huì)（ASA）Fellow，現(xiàn)任 IMS 理事會(huì)成員。2000年本科畢業(yè)于中國(guó)科技大學(xué)統(tǒng)計(jì)專業(yè)，2003年獲得加利福尼亞大學(xué)戴維斯分校統(tǒng)計(jì)學(xué)博士學(xué)位，曾任職于多倫多大學(xué)統(tǒng)計(jì)科學(xué)系終身教授?，F(xiàn)擔(dān)任Canadian Journal of Statistics的主編，至今擔(dān)任9個(gè)國(guó)際統(tǒng)計(jì)學(xué)核心期刊編委，包括統(tǒng)計(jì)學(xué)頂級(jí)期刊Journal of the American Statistical Association和 Annals of Statistics。

講座內(nèi)容：

We propose a new method for functional nonparametric regression with a predictor that resides on a finite-dimensional manifold but is only observable in an infinite-dimensional  space. Contamination of the predictor due to  discrete/noisy measurements is also accounted for.  By using functional local linear manifold smoothing, the proposed estimator enjoys a polynomial rate of convergence that adapts to the intrinsic manifold dimension and the contamination level. This is in contrast to the logarithmic convergence rate in the literature of functional nonparametric regression.  We also observe a phase transition phenomenon regarding the interplay of the manifold dimension and the contamination level. We demonstrate that the proposed method has favorable numerical performance relative to commonly used methods via simulated and real data examples.

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院