A variable selection criterion for linear discriminant rule and its optimality in high dimensional and large sample data
A variable selection criterion for linear discriminant rule and its optimality in high dimensional and large sample data
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线性判别规则的变量选择准则及其在高维大样本数据下的最优性
DOI：
10.1016/j.jmva.2013.10.005
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
T. Kubokawa
中科院分区：
文献类型：
--
作者：
Masashi Hyodo;T. Kubokawa
本文提出了一种新的变量选择方法，称为MEC，用于高维大样本下的线性判别规则。MEC是作为线性判别规则（LDR）的误分类错误概率的二阶无偏估计而导出的。结果表明，MEC不仅渐近分解成'拟合'和'惩罚'的条款，如AIC和Mallow CP，但也具有渐近最优的意义上，MEC实现最小的条件概率的误分类在候选变量集。通过仿真研究表明，MEC在选择真变量集的意义上具有良好的性能。
In this paper, we suggest the new variable selection procedure, called MEC, for linear discriminant rule in the high dimensional and large sample setup. MEC is derived as a second-order unbiased estimator of the misclassification error probability of the linear discriminant rule (LDR). It is shown that MEC not only asymptotically decomposes into ‘fitting’and ‘penalty’terms like AIC and Mallows C p, but also possesses an asymptotic optimality in the sense that MEC achieves the smallest possible conditional probability of misclassification in candidate variable sets. Through simulation studies, it is shown that MEC has good performances in the sense of selecting the true variable sets.