Statistics and Data Science Seminar
Jie Yang
MSCS of UIC
Sliced Inverse Moment Regression Using Weighted Chi-Squared
Abstract: We propose a new class of dimension reduction methods
using the first two inverse moments, called Sliced Inverse Moment
Regression (SIMR). We develop corresponding weighted chi-squared
tests for the dimension of the regression. Basically, SIMR are
linear combinations of Sliced Inverse Regression (SIR) and a new
method using candidate matrix M_{zz'|y}, which is designed to
recover the entire inverse second moment subspace. Theoretically,
SIMR, as well as Sliced Average Variance Estimate (SAVE), are more
capable of recovering the complete central dimension reduction subspace
than SIR and Principle Hessian Directions (pHd). Therefore it can
substitute for SIR, pHd, SAVE or any linear combination of them
at a theoretical level. Simulation study shows that SIMR using the
weighted chi-squared test may have consistently greater power than
SIR, pHd, and SAVE.
Wednesday February 14, 2007 at 3:30 PM in SEO 712