统计与管理学院2016年学术报告第19期
【主 题】Functional and very high dimension reduction
【报告人】 Ma Yanyuan 教授
University of South Carolina
【时 间】 2016年5月23日（星期一）15:00－16:00
【地 点】 上海财经大学统计与管理学院大楼1208室
【摘 要】To study the relation between a univariate response and multiple functional covariates, we propose a functional single index modelthat is semiparametric. The parametric part of the model integrates the linear regression modeling for functional data and the sucient dimension reduction structure. The nonparametric part of the model further allows the response-index dependence or the link function to be unspecied. We use B-splines to approximate the coecient function in the functional linear regression model part and reduce the problem to a familiar dimension folding model. We develop a new method to handle the subsequent dimension folding model by using kernel regression in combination with semiparametric treatment. The new method does not impose any special requirement on the inner product between the covariate function and the B-spline bases, and allows ecient estimation of both the index vector and the B-spline coecients. The estimation method is general and applicable to both continuous and discrete response variables. We further derive asymptotic properties of the class of methods for both the index vector and the coecient function. We establish the semiparametric optimality, which has not been done before in a semiparametric model where both kernel and B-spline estimation are involved.
【邀请人】 冯兴东
