Student Seminar Series - August 12, 2005
University of Minnesota
School of Statistics
College of Liberal Arts
Optimal
sufficient dimension reduction for the multivariate conditional mean in
multivariate regression
Jae Keun Yoo
Friday, August 12, 2005
10:00 AM, B80
Ford Hall
Minneapolis, East Bank Campus
Refreshments at 9:30 AM
300 Ford Hall
Abstract
Recently, Cook and Setodji (2003) developed a method for
sufficient dimension reduction in multivariate regressions by
estimating
the multivariate central mean space. Their test statistic for the
dimension of the multivariate central mean subspace is a weighted sum
of
independent chi-square random variables. We provide an optimal version
of
this method in the roughly same context. The test statistic for the
optimal version has a chi-square distribution asymptotically, and the
estimates of the multivariate central mean subspace are efficient.
Additionally, the optimal version allows tests of predictor effects. A
comparison of the two methods will be done and the asymptotic behaviors
of
predictor effect tests will be studied via simulations.