Sufficient dimension reduction and variable selection.

Abstract

Sufficient dimension reduction (SDR) in regression was first introduced by Cook (2004). It reduces the dimension of the predictor space without loss of information and it is very helpful when the number of predictors is large. It alleviates the “curse of dimensionality” for many statistical methods. In this thesis, we study the properties of a dimension reduction method named “continuum regression”; we propose a unified method – coordinate-independent sparse estimation (CISE) – that can simultaneously achieve sparse sufficient dimension reduction and screen out irrelevant and redundant variables efficiently; we also introduce a new dimension reduction method called “principal envelope models”.