Forward variable selection for sparse ultra-high-dimensional generalized varying coefficient models
Forward variable selection for sparse ultra-high-dimensional generalized varying coefficient models
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DOI：
10.1007/s42081-020-00090-z
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发表时间：
2020-09
影响因子：
1.3
通讯作者：
Toshio Honda;Chien-Tong Lin
中科院分区：
文献类型：
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作者：
Toshio Honda;Chien-Tong Lin
在本文中，我们提出了超高维广义变系数模型特征筛选的正向变量选择方法。我们使用回归样条法来逼近系数函数，然后最大化对数似然来依次选择另一个相关协变量。如果我们决定不再通过从我们的停止规则中选择任何新的协变量来显著改善对数似然，我们终止正向过程，并给出相关协变量的估计。在高维模型的顺序程序的停止规则中，忽略了当前模型大小的影响。我们的停止规则适当地考虑了当前模型的大小。在正则性条件下，我们的正演过程具有屏蔽相合性等一些理想性质。我们还给出了数值研究的结果，以显示它们良好的有限样本性能。
In this paper, we propose forward variable selection procedures for feature screening in ultra-high-dimensional generalized varying coefficient models. We employ regression spline to approximate coefficient functions and then maximize the log-likelihood to select an additional relevant covariate sequentially. If we decide we do not significantly improve the log-likelihood any more by selecting any new covariates from our stopping rule, we terminate the forward procedures and give our estimates of relevant covariates. The effect of the size of the current model has been overlooked in stopping rules for sequential procedures for high-dimensional models. Our stopping rule takes into account the size of the current model suitably. Our forward procedures have screening consistency and some other desirable properties under regularity conditions. We also present the results of numerical studies to show their good finite sample performances.