Authors

• Chunming Zhang
• Zhengjun Zhang
• Yi Chai

Abstract

Variable selection via penalized estimation is appealing for
dimension reduction. For penalized linear regression, Efron, et al. (2004)
introduced the LARS algorithm. Recently, the coordinate descent (CD)
algorithm was developed by Friedman, et al. (2007) for penalized linear
regression and penalized logistic regression and was shown to gain computational
superiority. This paper explores the CD algorithm to penalized
Bregman divergence (BD) estimation for a broader class of models,
including not only the generalized linear model, which has been well
studied in the literature on penalization, but also the quasi-likelihood
model, which has been less developed. Simulation study and real data
application illustrate the performances of the CD and LARS algorithms
in regression estimation, variable selection and classification procedure
when the number of explanatory variables is large in comparison to the
sample size.

Keywords

• Bregman divergence
• LARS algorithm
• quasi-likelihood
• sparsity
• Taylor expansion
• variable selection