Abstract #301048

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JSM 2002 Abstract #301048
Activity Number: 101
Type: Topic Contributed
Date/Time: Monday, August 12, 2002 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract - #301048
Title: Variable Selection for Generalized Linear Models via an MM Algorithm
Author(s): David Hunter*+
Affiliation(s): Pennsylvania State University
Address: 310 Thomas Building, University Park, Pennsylvania, 16802, USA
Keywords: EM algorithm ; MM algorithm ; penalized likelihood ; SCAD ; variable selection
Abstract:

A class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed by Fan and Li (2001). Maximizing the nonconcave penalized likelihood function is very challenging, as it is a nonconcave function with singularities. A new algorithm, which repairs the drawback of Fan and Li's algorithm, is proposed for finding a maximizer of the penalized likelihood via a modified local quadratic approximation. We discuss a class of algorithms called MM, or minorize-maximize, algorithms---of which the well-known class of EM algorithms is a subset---and demonstrate that the modified local quadratic approximation algorithm is an example of an MM algorithm. This enables us to analyze the convergence properties of the algorithm using techniques applied to EM, and more generally MM, algorithms. We conduct some simulation studies and investigate some applications of the algorithm.

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