Asymptotic Expansion of the Misclassification Probabilities of D- and A-Criteria for Discrimination from Two High Dimensional Populations Using the Theory of Large Dimensional Random Matrices
Asymptotic Expansion of the Misclassification Probabilities of D- and A-Criteria for Discrimination from Two High Dimensional Populations Using the Theory of Large Dimensional Random Matrices
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DOI：
10.1006/jmva.1993.1054
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发表时间：
1993-07
影响因子：
1.6
通讯作者：
H. Saranadasa
中科院分区：
文献类型：
--
作者：
H. Saranadasa
在本文中，实验设计的一些想法被用于判别分析。通过将总体视为组，可以通过在将其分配给每个组之后最小化组内平方和和叉积矩阵的合适范数来对新观察进行分类。基于 D 准则的分类与基于最大似然比准则的分类相同。对于测量空间 (p) 几乎等于总样本大小 (n) 的高维设置，A 准则的性能优于 D 准则。使用埃奇沃斯展开推导出近似的误分类错误概率，结果表明这些概率与模拟结果非常吻合。
In this paper some ideas on experimental designs are used in discriminant analysis. By considering the populations as groups, one may classify a new observation by minimizing a suitable norm of the within groups sum of squares and cross products matrix after assigning it to each group. The classification based on the D-criterion is identical to that based on the maximum likelihood ratio criterion. For a high dimensional setting with measurement space (p) nearly equal to the total sample size (n), the A-criterion performs better than the D-criterion. Approximate misclassification error probabilities were derived using Edgeworth expansions and it is shown these agree closely with simulated results.