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Variable selection in nonparametric additive models

Variable selection in nonparametric additive models

This video was recorded at Workshop on Sparsity and Inverse Problems in Statistical Theory and Econometrics, Berlin 2008. We consider a nonparametric additive model of a conditional mean function in which the number of variables and additive components may be much larger than the sample size but the number of non-zero additive compo- nents is small relative to the sample size. The statistical problem is to determine which additive components are non-zero. The additive compo- nents are approximated by truncated series expansions with B-spline bases. The adaptive group LASSO is used to select non-zero components. We give conditions under which this procedure selects the non-zero components correctly with probability approaching one as the sample size increases. Fol- lowing model selection, oracle-eļ¬ƒcient, asymptotically normal estimators of the non-zero components can be obtained by using existing methods. The results of Monte Carlo experiments show that the adaptive group LASSO procedure works well with samples of moderate size.


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