Additive model selection
Anestis Antoniadis and
Italia De Feis ()
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Umberto Amato: National Research Council
Anestis Antoniadis: Université Joseph Fourier
Italia De Feis: National Research Council
Statistical Methods & Applications, 2016, vol. 25, issue 4, 519-564
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.
Keywords: Additive models; Dimension reduction; Penalization; Hypothesis test; Backfitting; Primary 62H12; 62G08; Secondary 62G10 (search for similar items in EconPapers)
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