Student Seminar Series -
September 27, 2007
University of Minnesota
School of Statistics
College of Liberal Arts
Principal Fitted Components on Small Samples
Kofi Placid Adragni
Tuesday, September 27, 2007
10 AM,
300
Ford Hall
Minneapolis, East Bank Campus
Refreshments
at 9:30 PM
300 Ford Hall
Abstract
In various scientific fields, researchers are confronted with large
datasets where there are many measured variables and few observations.
With the presence of a measured outcome, possible regressions face a
challenge due to the number of predictors exceeding the number of
observations. Several methods are available to get round or deal with
the challenge.
Cook (2007) introduced the use of Principal Components (PC) and
Principal Fitted Components (PFC) models in the inverse regression
setting as an approach for dimension reduction. The development of the
PFC model suggests a large sample (n>p) and also involves the use of
basis functions. In the first part of this proposal, we explore various
basis functions to be used in the PFC model. Using univariate PFC model,
a method called Screening by Principal Fitted Components (SPFC) is
derived to aid in selecting predictors related to the outcome. The
relationship between the response variable and individual predictors can
be complex, not necessarily linear.
In the second part, we investigate a modeling scenario where the
information on an outcome may accumulate when the number of predictors
gets large. An extended PFC model is used. The maximum likelihood
estimators of the parameters in the model are derived and the sufficient
reduction of the predictors' subspace is obtained.