On Single-Index Models.  -- High Dimensional Data
   Yan Yu

Abstract: Single-index models are an important tool for multivariate 
nonparametric estimation. By reducing the dimensionality from that 
of a general covariate vector to a univariate index, single-index 
models avoid the so-called "curse of dimensionality." Firstly, I 
will give a brief overview of single-index models, focusing on 
generalized partially linear single-index regression models by a 
penalized spline approach (P-spline). Secondly I will introduce 
single-index varying coefficient models for both 
regression and dependent data, where we focus on the estimation, 
inference, and forecasting of the single-index coefficient 
models under dependence. Finally I will discuss some most recent 
research for single-index conditional quantiles using local 
linear estimation. 

Related working papers are downloadable from 
http://statqa.cba.uc.edu/~yuy/index.htm