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Additive model selection

Author

Listed:
  • Umberto Amato

    (National Research Council)

  • Anestis Antoniadis

    (Université Joseph Fourier
    University of Cape Town)

  • Italia De Feis

    () (National Research Council)

Abstract

We study sparse high dimensional additive model fitting via penalization with sparsity-smoothness penalties. We review several existing algorithms that have been developed for this problem in the recent literature, highlighting the connections between them, and present some computationally efficient algorithms for fitting such models. Furthermore, using reasonable assumptions and exploiting recent results on group LASSO-like procedures, we take advantage of several oracle results which yield asymptotic optimality of estimators for high-dimensional but sparse additive models. Finally, variable selection procedures are compared with some high-dimensional testing procedures available in the literature for testing the presence of additive components.

Suggested Citation

  • Umberto Amato & Anestis Antoniadis & Italia De Feis, 2016. "Additive model selection," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(4), pages 519-564, November.
  • Handle: RePEc:spr:stmapp:v:25:y:2016:i:4:d:10.1007_s10260-016-0357-8
    DOI: 10.1007/s10260-016-0357-8
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    References listed on IDEAS

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    1. Xia Cui & Heng Peng & Songqiao Wen & Lixing Zhu, 2013. "Component Selection in the Additive Regression Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 491-510, September.
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