Special Lecture Series:
Dimension Reduction in Regression
by
Visiting Prof. Lixing Zhu
Chair Professor and Department Head
Department of Mathematics
Hong Kong Baptist University
This lecture series consists of three lectures to introduce high-dimensional semiparametric regression estimation procedures as follows
September 29, 2014- Lecture 2
Dimension reduction estimation: can linear methods solve nonlinear problems?
In this lecture, we introduce two approaches to identify and estimate the central subspace, or equivalently, the base vectors of the subspace. Interestingly we will show that under certain regularity conditions, the ordinary least squares method (OLS) that is for linear regression models can be well applied to identify one of the base vectors. It is particularly useful when underlying model has only one such vector. The examples of models include some nonlinear and even semiparametric models such as generalized linear models, transformation models and single-index models. Further, another moment-based method called the principal Hessian direction (pHd) is introduced which can identify and estimate more than one base vector. Both need no nonlinear or nonparametric estimation procedure even underlying models are nonlinear and semiparametric.
For more information, contact: Tracy Burke at tracy.burke@uconn.edu