Variable selection in nonparametric additive models

author: Joel Horowitz, Northwestern University
published: Dec. 18, 2008,   recorded: December 2008,   views: 4657


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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-efficient, 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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