Penalized estimation in additive varying coefficient models using grouped regularization
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Additive varying coefficient models are a natural extension of multiple linear regression models, allowing the regression coefficients to be functions of other variables. Therefore these models are more flexible to model more complex dependencies in data structures. In this paper we consider the problem of selecting in an automatic way the significant variables among a large set of variables, when the interest is on a given response variable. In recent years several grouped regularization methods have been proposed and in this paper we present these under one unified framework in this varying coefficient model context. For each of the discussed grouped regularization methods we investigate the optimization problem to be solved, possible algorithms for doing so, and the variable and estimation consistency of the methods. We investigate the finite-sample performance of these methods, in a comparative study, and illustrate them on real data examples.
KeywordsGrouped Lasso regularization Multiple linear regression models Variables selection Varying coefficient models
The authors thank the editor and two reviewers for their detailed reading of the manuscript and their valuable comments and suggestions that led to a considerable improvement of the paper. Support from the IAP Research Network nr. P6/03 and P7/06 of the Federal Science Policy, Belgium, is acknowledged. The second author also gratefully acknowledges financial support by the projects GOA/07/04 and GOA/12/014 of the Research Fund KULeuven and the FWO-Project G.0328.08N of the Flemish Science Foundation.
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