Student Seminar Series - June 2, 2005
University of Minnesota
School of Statistics
College of Liberal Arts

Optimal Sufficient Dimension Reduction in Regression with Categorical Predictors


Xuerong Wen


Thursday, June 2, 2005
10:00 AM, 115 Ford Hall
Minneapolis, East Bank Campus

Refreshments at 9:30 AM
300 Ford Hall


Abstract

Recent advances in data collection and storage capabilities have resulted in huge amount of data being collected at a very rapid rate. In the context of regressions, sufficient dimension reduction is aiming to replace the high-dimensional predictors with a minimal set of linear combinations of the predictors, without loss of information on the regression and without requiring a pre-specific parametric model.

Under the restriction that the covariance matrices of the continuous predictors be constant across the levels of the categorical predictor, Chiaromonte, Cook and Li (2002, Annals of Statistics) introduced partial sufficient dimension reduction to regressions with both continuous and categorical predictors. We propose a new estimation method via a minimum discrepancy approach without this restriction. Our method is optimal in terms of asymptotic efficiency and its test statistic for testing the order of the dimension reduction subspace always has an asymptotic chi-squared distribution. It also gives us the ability to test predictor effects without assuming a model. We also show that the estimates proposed by Chiaromonte, et al. can be recast as minimizers of a quadratic discrepancy function. Simulation studies show that our method is superior to the previous one even when the homogenous covariance condition holds.