Penalized Bregman Divergence Estimation via Coordinate Descent

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.