New Tools for Regression Analysis: Dimension Reduction and Inverse Regression

Instructor(s):

• Sanford Weisberg, Statistics, University of Minnesota

Dimension reduction in regression takes one of two forms: variable selection, in which predictors are dropped, and variable combination, in which predictors are combined into indices thereby reducing dimension. The familiar methods for selection include stepwise methods, all subsets methods, criterion based methods like AIC, and regularization methods like the lasso, while principal component regression is the most common indexing method. All these methods assume a known model or class of models.

In this series of lectures we approach dimension reduction in a model-free setting, and seek to reduce dimension by both deletion and indexing, given minimal assumptions concerning the dependence of the response on the predictors. Model based or nonparametric methods can be applied to the lower dimensional problem. The methods to be discussed are based on inverse regression of the predictors on the response. All the methods presented in these lectures are implemented in the "dr" package in R, and use of this package will be illustrated.

Dates:  July 13-15 

Fee:  consult the fee structure