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Activity Number:
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146
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Type:
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Invited
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Date/Time:
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Monday, August 3, 2009 : 10:30 AM to 12:20 PM
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Sponsor:
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IMS
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| Abstract - #302904 |
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Title:
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Variable Selection in Nonparametric Additive Models
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Author(s):
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Jian Huang*+ and Joel Horowitz and Fengrong Wei
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Companies:
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The University of Iowa and Northwestern University and The University of Iowa
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Address:
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Department of Statistics and Actuarial Science, Iowa City, IA, 52242,
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Keywords:
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Adaptive group Lasso ; Component selection ; High-dimensional data ; Nonparametric regression ; Oracle property ; Sparse model
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Abstract:
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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 larger than the sample size but the number of non-zero additive components is "small" relative to the sample size. The statistical problem is to determine which additive components are non-zero. The additive components are approximated by truncated series expansions with B-spline bases. With this approximation, the problem of component selection becomes that of selecting the groups of coefficients in the expansion. We apply the adaptive group Lasso to select nonzero components, using the group Lasso to obtain an initial estimator and reduce the dimension of the problem. We give conditions under which the group Lasso selects a model whose number of components is comparable with the underlying model.
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