Asymptotic relative efficiency of the linear discriminant function under partial nonrandom classification of the training data
Asymptotic relative efficiency of the linear discriminant function under partial nonrandom classification of the training data
复制标题
训练数据部分非随机分类下线性判别函数的渐近相对效率
DOI：
10.1080/00949659508811689
复制
发表时间：
1995
影响因子：
1.2
通讯作者：
D. Scot
中科院分区：
文献类型：
--
作者：
G. McLachlan;D. Scot
本文考虑的问题，线性判别规则是由训练数据，只有部分分类的两组原产地。另一个复杂的问题是，来源不明的数据并不构成从两个基本群体的混合物中观察到的随机样本。在同方差正态模型的假设下，由部分分类的训练数据的最大似然形成的样本线性判别规则的总错误率导出，并包括在单变量特征数据的情况下的第一阶的条款。这样形成的样本规则的这种一阶扩展被用来定义其相对于从完全分类的随机训练集形成的规则以及从完全未分类的随机集形成的规则的渐近效率。
This paper considers the problem where the linear discriminant rule is formed from training data that are only partially classified with respect to the two groups of origin. A further complication is that the data of unknown origin do not constitute an observed random sample from a mixture of the two underlying groups. Under the assumption of a homoscedastic normal model, the overall error rate of the sample linear discriminant rule formed by maximum likelihood from the partially classified training data is derived up to and including terms of the first order in the case of univariate feature data. This first-order expansion of the sample rule so formed is used to define its asymptotic efficiency relative to the rule formed from a completely classified random training set and also to the rule formed from a completely unclassified random set.