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Activity Number: 383
Type: Topic Contributed
Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
Sponsor: Biometrics Section
Abstract - #304251
Title: PFC Models with a Heterogenous Error Structure
Author(s): Kofi Placid Adragni*+
Companies: University of Maryland Baltimore County
Address: 302 Cedar Run Place, Catonsville, MD, 21228, United States
Keywords: Sufficient dimension reduction ; Inverse regression ; Variable selection ; Grassmann manifold ; High dimensionality ; Multivariate analysis
Abstract:

Principal fitted components models (PFC; Cook, RD (2007): Fisher Lecture. Dimension Reduction in Regression. Statistical Science, Vol. 22, No. 1, 1-26.) are likelihood-based methods for dimension reduction in regression. Given a p-vector predictor X and a response Y, PFC models aim at obtaining a sufficient reduction R(X) of dimension less than p, that retains all the regression information of Y contained in X. When the number of predictors p is large or larger than the number of observations n, the initial development of PFC does not allow to model predictors that, conditionally on the response, are dependent. We expand the applicability of PFC models with an heterogenous structure of the error in the model of X|Y to allow a conditional dependency among some predictors when p is large. The sufficient reduction was obtained using an efficient Grassmann manifold optimization procedure.


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