【专家简介】： 桑培俊，从2018年起在加拿大滑铁卢大学担任助理教授。在Biometrics, Statistica Sinica, Journal of Computational and Graphical Statistics等统计杂志发表过多篇文章。主要研究方向是函数型数据和实时数据，尤其是函数型数据分析回归模型中的统计推断问题以及实时函数型数据的回归问题。
【报告摘要】： We propose a nonlinear function-on-function regression model where both the covariate and the response are random functions. The nonlinear regression is carried out in two steps: we first construct Hilbert spaces to accommodate the functional covariate and the functional response, and then build a second-layer Hilbert space for the covariate to capture nonlinearity. The second-layer space is assumed to be a reproducing kernel Hilbert space, which is generated by a positive kernel determined by the inner product of the first-layer Hilbert space for $X$--this structure is known as the nested Hilbert spaces. We develop estimation procedures to implement the proposed method, which allows the functional data to be observed at different time points for different subjects. Furthermore, we establish the convergence rate of our estimator as well as the weak convergence of the predicted response in the Hilbert space. Numerical studies including both simulations and a data application are conducted to investigate the performance of our estimator in finite sample.
时 间：2023年7月4日 10:00
地 点：位育楼417+线上（腾讯会议号437347265）
