VARIABLE SELECTION IN NONPARAMETRIC ADDITIVE MODELS.
VARIABLE SELECTION IN NONPARAMETRIC ADDITIVE MODELS.
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DOI：
10.1214/09-aos781
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发表时间：
2010-08-01
影响因子：
4.5
通讯作者：
Wei F
中科院分区：
文献类型：
--
作者：
Huang J;Horowitz JL;Wei F
我们考虑一个条件均值函数的非参数可加性模型，其中变量和可加性成分的数量可能大于样本大小，但非零可加性成分的数量相对于样本大小是“小”的。统计问题是确定哪些可加性分量是非零的。加法分量通过B样条基的截断级数展开来逼近。在这种近似下，分量选择的问题就变成了选择展开式中的系数组的问题。我们应用自适应组Lasso来选择非零分量，使用组Lasso来获得初始估计并降低问题的维数。我们给出的条件下，组Lasso选择一个模型，其组件的数量是与基础模型相媲美，和自适应组Lasso选择正确的非零组件的概率接近1作为样本大小的增加，并达到最佳的收敛速度。Monte Carlo实验结果表明，自适应组Lasso过程适用于中等规模的样本。最后通过一个算例说明了该方法的应用。
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 nonzero additive components is “small” relative to the sample size. The statistical problem is to determine which additive components are nonzero. 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, and the adaptive group Lasso selects the nonzero components correctly with probability approaching one as the sample size increases and achieves the optimal rate of convergence. The results of Monte Carlo experiments show that the adaptive group Lasso procedure works well with samples of moderate size. A data example is used to illustrate the application of the proposed method.