Student Seminar Series - May 9, 2005
University of Minnesota
School of Statistics
College of Liberal Arts
A
Power Study of Some Dimension Reduction Regression Methods
Jorge De la Vega Gongora
Monday, May 9, 2005
10:00 AM, 127
Ford Hall
Minneapolis, East Bank Campus
Refreshments at 9:30 AM
300 Ford Hall
Abstract
We present results of a numerical study including power of
dimension reduction
methods that are concerned with estimating the mean function in a
regression
context. In particular, it will compare two methods: principal Hessian
directions (pHd) to the iterative Hessian transformations (iht).
The goal is to implement the iterative Hessian transformation method
and the
corresponding tests in R, find conditions where the application of one
particular method is better than the others, find how robust the
methods are
when the assumptions of each method are not satisfied and learn more
about
the behavior of these methods.
The power of the statistical tests for dimension depend on many
characteristics
like the sample size, the distribution of the errors, the number and
the joint
distribution of the predictors and the shape of the mean function.
There is substantial literature on dimension reduction regression
methods. We
concentrate on methods that estimate only the mean function and not on
more
general methods that estimate higher moments. Inverse regression
methods play
an important role in the approach of dimension reduction to regression
analysis. They allow to make inference about the dimension of the
central
subspace, the main tool for inference of the dimension of a regression
model,
but the tests are based on many assumptions and restrictions that might
not be
satisfied in real data sets and therefore it is sensible to study how
departure
of the assumptions affect the inference paradigm.