A consistent variable selection method in high-dimensional canonical discriminant analysis
A consistent variable selection method in high-dimensional canonical discriminant analysis
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DOI：
10.1016/j.jmva.2019.104561
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发表时间：
2020
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影响因子：
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通讯作者：
Ryoya Oda;Yuya Suzuki;H. Yanagihara;Y. Fujikoshi
中科院分区：
文献类型：
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作者：
Ryoya Oda;Yuya Suzuki;H. Yanagihara;Y. Fujikoshi
本文给出了典型判别分析中基于广义信息准则的变量选择方法一致性的充分条件。为了检验一致性属性，我们使用了一个高维渐近框架，使得当样本大小n趋于无穷大时，即使观测向量的维数也趋于无穷大，观测向量p的长度与样本大小的比率p scinn也收敛到小于1的常数。利用导出的条件，我们提出了一个一致的变量选择方法。从数值模拟，我们表明，我们提出的方法选择的真实模型的概率是高的，即使当p是大的。最后，通过一个真实的数据验证了该方法的有效性.
In this paper, we obtain the sufficient conditions to determine the consistency of a variable selection method based on a generalized information criterion in canonical discriminant analysis. To examine the consistency property, we use a high-dimensional asymptotic framework such that as the sample size n goes to infinity, then the ratio of the length of the observation vector p to the sample size, p∕ n, converges to a constant that is less than one even if the dimension of the observation vector also goes to infinity. Using the derived conditions, we propose a consistent variable selection method. From numerical simulations, we show that the probability of selecting the true model by our proposed method is high even when p is large. Further, the advantage of the proposed method is demonstrated by a real data.