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Activity Number: 401
Type: Contributed
Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Computing
Abstract - #305228
Title: Variable Selection Algorithms for the Proportional Odds Model
Author(s): Xizhen Cai*+ and David Hunter
Companies: Penn State University and Penn State University
Address: 325 Thomas Building, State College, PA, 16802, United States
Keywords: penalized profile likelihood ; consistency ; MM algorithms ; ICM algorithms

Variable selection via a penalized likelihood approach has been used for generalized linear models, and corresponding estimates enjoy an oracle property (Fan and Li, 2001). We discuss the problem of variable selection for a sparse proportional odds model, which is a semi-parametric model, and penalized profile likelihood is maximized to estimate and select variables simultaneously. We show under certain regularity conditions that the estimates for nonzero coefficients are normally distributed, while those for zero coefficients are nearly n-consistent. These results are derived using an expansion for the profile likelihood function by Murphy and Van der Vaart (2000), so they can be easily generalized to a much broader range of semi-parametric models. We also provide a further condition on the smoothness of the profile likelihood functions that guarantees sparse estimates. In addition, various algorithms to maximize the penalized likelihood estimator are proposed based on MM algorithm framework.

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